Category: Science

Introduction

Electric charge is an intrinsic property of matter that allows it to experience a force when placed in an electric field. Charges are classified into two types or signs: positive, and negative. You can create a simple charged object by rubbing a balloon against your hair, which transfers charges from one body to another. This is what gives rise to static electricity, so named because there is no “flow” of charges here. You can do the same with carpets and other woollen items. In this article, we will discuss electric charges in detail.

Electric Charge Definition

Electric charge is a natural property of matter that allows it to experience a force when placed in an electric or magnetic field. It is a scalar quantity with no direction but it is classified into positive and negative types. 

Typically, charges are created via the transfer of electrons and the body that donates electrons is said to be positively charged, while the one that receives it becomes negatively charged. Just like magnets, like charges repel each other and opposite charges attract. Electrons are present in the atoms of every single element and thus, atoms are neutral as a whole, meaning that they carry no net charge. However, objects can gain charge via the transfer of electrons. Mathematically, the charge on an electron is equal to \(\;{\bf{1}}.{\bf{6}} \times {\bf{1}}{{\bf{0}}^{ – {\bf{19}}}}{\bf{C}}\). Further, charge is always transferred as an integral multiple of this quantity. That is, the charge on any object must be:

Q=ne

Q=total charge

e= charge on electron

n= number of electron

Basic properties of electric charge

Conservation of electric charge: Just like mass and energy always remain conserved in nature, electric charge is also a fundamental quantity that can never be created or destroyed. Rather, it is only transferred from body to body.

Example: Let us assume we have 15 C of charge on an object. We can redistribute it across several objects in any way we want, but we cannot make this charge vanish into nothingness.

Additive nature of electric charges: Since charges are scalar quantities, multiple charges on a system can be added algebraically.

For a system containing n number of charges \({q_1},{q_2},{q_3},…………{q_n}\), the total charge would be

\(Q = {q_1} + {q_2} + {q_3} + …………{q_n}\)

Note that if some of the charges are negative, that sign must be taken into account.

Quantization of electric charge: Since charge is always transferred as an integral multiple of the charge on one electron (represented by e), the total charge on any system is always quantized in units of e.

Q=ne

Transfer of charges: Charged bodies, when brought in contact, can exchange charges. That is, charge can flow across materials in contact in order for there to be equilibrium.

Like charges repel: Like charges repel each other. This fundamental property of charges is an essential force that keeps the universe stable and without it, nothing in this world would exist.

Like charges repel

Unlike charges attract: Just like magnets, unlike charges attract. This is what allows electrons to remain in orbit and thus, anything in this world to exist.

Linkage with mass: Charges cannot exist nowhere and must be present on some body.

Charge is invariant: Regardless of how fast a body moves and what frame of reference its speed is measured in, the charge on it remains the same.

Electromagnetic properties: Charges at rest produce an electric field and those in motion, produce a magnetic field. When charges are accelerated, they produce an electromagnetic field and give rise to electromagnetic radiation.

The Unit of Electric charge

The SI unit of the electric charge is coulomb, which is denoted by C, and in the CGS unit, it is measured in electrostat unit.

\(1C = \;3 \times {\bf{1}}{{\bf{0}}^{\bf{9}}}{\bf{C}}\)

Electric charge and field

When placed in an electric field, all electric charges experience a force, whose magnitude is given by the following relation:

F=qE

The sign of the charge and the direction of the electric field together decide the direction of this force. Note that E here represents the value of electric field and q is the charge placed inside it. For positive charges, the force is along the direction of the electric field and for negative ones, it is opposite. Note that this also allows us to define electric field as the force experienced per unit charge with SI units of N/C. That is,

\(E = \frac{F}{q}\)

Summary 

This article described the concept of electric charge along with its properties and units. Electric charge is an inherent property of matter that allows bodies to experience a force in the presence of a magnetic field. Charges themselves are attracted to unlike charges and repel like ones. This property of charge is what keeps the universe stable.

 

Frequently Asked Questions

1. How can we generate charged bodies?

We can generate charged bodies via friction, induction, or by conduction.

2. Write down the dimensional formula of the electric charge.

As such, charge has no inherent dimensions. Instead, the formula of current allows us to write its dimensions.

\(Q = I \times t\)

Thus, the dimensions of charge are \(\left[ {{M^0}{L^0}{T^1}{A^1}} \right]\).

3. Give examples of positive, negative, and neutral bodies.

Atoms yield the best example here. All electrons inside them are negatively charged, while the protons are positively charged. However, the neutrons carry no charge and thus are neutral.

4. Write down the practical unit of charges.

Practically, a common unit of charge used is Ampere hour.

1 Amp hr = 3600 C

5. Write the definition of electric field

The electric field is a property by virtue of which, a charged object can exert electric field on other charged objects in its vicinity. It is defined as the force per unit charge.

Introduction

In simple terms, force is just a way for two objects to interact. Its effect is that of a push or pull and it causes a change in the position and/or velocity of the object it is being applied on. The application of force also lends us the possibility of doing work as the object gets displaced.

Force is a vector quantity and thus, has both magnitude and direction. Therefore, for two forces to be truly equal, they must have the same magnitude and be applied in the same direction. When two forces of the same magnitude are applied on a body in opposite directions, they are said to be balanced. In such a case, the net force on the body is zero. An unbalanced force is encountered when the net force on the body isn’t zero.

What are Balanced Forces?

Balanced forces are those that act on a system with equal magnitude but in opposite directions. This results in a net force of zero on the system, causing it to remain in the state it was in (either at rest or in motion) with zero acceleration. In such a state, the body is said to be in equilibrium.

Example: Let’s consider four forces acting on the rectangular box the below diagram

Example of balanced forces.

The diagram attached below shows a rectangular box subject to four forces: 

• In the vertical direction, there is an upward force of 3 Newtons and a downward force of 3 Newtons. Since these forces are equal in magnitude but opposite in directions, they cancel each other out and result in no net force in the y-direction. 
• Similarly, the forces in the x-direction have equal magnitude but are in opposite directions, making them balanced as well. Thus, the rectangular box is experiencing balanced forces.

Examples of Balanced Forces

• Tug of war in which teams have equal members – The idea of tug of war is to pull the reference point on the rope beyond your line. However, if two identical teams were to play tug of war, they would exert identical forces on the rope, but in opposite directions. Thus, the rope would remain at rest and we have a state of balanced forces.
• Book on the table – A book when placed on a table is in equilibrium since its weight and the normal reaction due to the table cancel each other out.
• Person standing on the ground – When we stand still, we exert a force on the ground equal to our weight, and the ground exerts a normal reaction on us. Thus, we are in a state of equilibrium under balanced forces.

Characteristics of Balanced Force

• The state of rest or of motion of the body is not altered when it experiences balanced forces.
• A system under balanced forces is in static equilibrium.
• The net force on the system is zero when it is experiencing balanced forces.

Effect of a Balanced Force on a Body

When a body experiences balanced forces, the net or resultant force acting on the body is zero. This means that balanced forces do not cause any change in the state of the body. If the body is at rest, it will remain at rest under the balanced force, and if the body is in motion, it will continue to move at the same velocity.

What are Unbalanced Forces?

An unbalanced force is one that causes a change in the motion of a body. If the body is at rest, an unbalanced force can set it in motion and vice versa, if the body is already in motion, an unbalanced force can change its speed or direction. 

When two forces acting on a body have unequal magnitudes, the system is under unbalanced force. The resultant force on the body is not zero, resulting in non-zero acceleration and an absence of equilibrium condition.

Example: Suppose a book is placed on a table that has an incline. In that case, it will begin sliding down

A book placed on a table

In the vertical direction, the table experiences the vertical component of the book’s weight and applies a normal reaction on the book. These forces balance each other out, but in the horizontal direction, the frictional force cannot balance the horizontal component of the book’s weight and thus, the book begins to slide down.

Examples of Unbalanced Forces

• Tug of war in which teams have unequal members – For a tug of war game where the two teams aren’t identical, one of them will apply a larger amount of force and end up winning the same.
• See saw the game – Since the two people sitting on the see-saw don’t have identical weights, this is an example of unbalanced force. 
• Kicking a ball – A ball receiving a kick receives an unbalanced force.

Difference between Balanced and Unbalanced Forces

Summary

This article explains the concept of forces and their two main types: balanced and unbalanced forces. Balanced forces do not affect the state of an object, whereas unbalanced forces are responsible for its motion. 

A body under the effect of balanced forces experiences no net acceleration or force, but unbalanced forces can cause net acceleration in the system. Another major difference is that balanced forces can only alter the geometry (shape or size) of the object, whereas unbalanced forces can also alter its state of motion.

Frequently Asked Questions

1. What are the possible states of motion?

The two states of motion are as follows:

1. A body can remain at rest, which is when it has no motion with respect to a reference point.
2. The second state is that of motion wherein, the body is moving with a certain velocity.

2. Can a balanced force deform a body?

Yes. While movement isn’t possible due to balanced forces, the geometry of the object can get altered.

3. Given acceleration, how do we find force?

According to Newton’s second law, force is equal to mass times the acceleration. That is,

F=ma

4. What unit is force measured in?

The S.I. unit of the force is newton or \({kgms^{-2}}\). In C.G.S. system, it is dyne or \({gcms^{-2}}\).

5. Give one daily life example of balanced force.

Screws or clips experience frictional force from the wall. This allows us to hang items on the walls which experience balanced forces and thus, do not fall down.

Introduction

The concept of pressure plays an integral role in our daily activities. For instance, a knife edge exerts a large amount of pressure on fruits and vegetables. While the science behind it may be new for some people, this occurs because the edge of the knife is very sharp. Surfaces that have small areas exert larger amounts of pressure and it is this property that enables us to cut fruits and vegetables using knives.

It is also pressure that allows various other devices like pumps and vacuum cleaners to function.

What is Pressure?

Pressure is the term used to describe the force applied on an object per unit area of the surface in a perpendicular direction and thus, it can be expressed as the ratio of force to area. Most commonly, we use the symbol ‘p’ to denote pressure and measure in the Sl unit of Pascal (Pa). In CGS systems, its unit is barye (Ba). Note that it is a scalar quantity with only magnitude and no direction.

For liquids, we define a quantity known as thrust. It is the total force acting on the surface of a solid that is touching the liquid. Thus, it has the same units as force and the formula also doesn’t differ:

\[thrust = pressure \times area\]

Hence, for liquids, we can also find pressure as thrust per unit area.

Pascal’s law states that pressure in a liquid is transmitted equally in all directions and thus, pressure at any point is unaffected by the shape of the vessel. The pressure exerted by the liquid at any given point is uniform and the force exerted by a liquid at rest is always normal to the surface in contact with it. 

Mathematically, the pressure at any point within the liquid is directly proportional to its density as well as the height of the liquid column above it. Hence, we can relate pressure at any point in a liquid column to these two quantities via the relation

\[{\bf{p}} = {\bf{h}}\rho {\bf{g}}\]

Here, is the density of the liquid, h is the height above it, and g is acceleration due to gravity.

Types of Pressures

1. Absolute Pressure:

Absolute pressure is the measurement of pressure in vacuum or empty space. It is measured from the absolute zero or absence of pressure and may be given as the combination of atmospheric and gauge pressure.

Absolute pressure = Atmospheric pressure + Gauge pressure

As an example, if we have

 Gauge pressure = 14 psi

 Atmospheric pressure = 30.5 psi

Absolute pressure = 14+ 30.5=44.5 psi

2. Gauge Pressure:

Gauge pressure refers to the pressure that is measured above the atmospheric pressure. When the atmospheric pressure is low, the gauge pressure will have a positive value, and vice versa. We can measure gauge pressure via the use of instruments known as manometres and gauges.

 Gauge pressure = Absolute pressure – Atmospheric pressure

3. Differential Pressure:

As implied by the name, differential pressure is a measure of the pressure difference that exists between two points. If \({P_{a}}\) and \({P_{b}}\) are pressures at two points a and b, then the differential pressure is given as

Venturi tube is a device that can best demonstrate the concept of differential pressure. It is used to measure the flow of fluids and can change the pressure in the middle, making it best suited to measure liquid pressure.

4. Sealed Pressure or Vacuum Pressure:

Vacuum is defined as a portion of space wherein there exists no matter and thus, it has zero pressure. Practically, such a condition is hard to achieve but a close enough situation may be arrived at by using sealed containers made of very strong materials.

What is Gauge Pressure?

Pressure measured over the atmospheric pressure is known as gauge pressure and it can be calculated as follows:

Local atmospheric pressure = 14.2psi

Absolute pressure = 28 psi

 Gauge pressure = Absolute pressure – Atmospheric pressure   

Gauge pressure= 28-14.2=13.8psi

Sometimes, we also refer to it as overpressure. It gives us an idea about the atmospheric weight of a point and is different under different weather conditions and sea level.

Relation Between Atmospheric Pressure and Gauge Pressure:

Pressure exerted by the atmosphere at any point is referred to as atmospheric pressure. The atmosphere is composed of a mixture of various gases and these gases exert a pressure due to the weight of the molecules above it. 

We can relate gauge pressure and atmospheric pressure via the absolute pressure

Gauge pressure = Absolute pressure – Atmospheric pressure  

Since absolute pressure is fixed, gauge pressure must become negative if the atmospheric pressure exceeds a certain threshold and vice versa.

Difference between Absolute and Gauge Pressure

Summary

Pressure is something fundamental that we experience in our everyday activities but often fail to notice. From cutting fruits with a knife-edge to breaking stones using chisels, our actions involve some level of pressure in one way or another. The amount of pressure required to do some task depends on where and how the force or thrust is applied as well as the area it is applied on. Mathematically, pressure is given as the ratio of force and area and thus, is higher for smaller areas.

Frequently Asked Questions

1. Explain the Bourdon Gauge instrument?   

This instrument can directly measure gauge pressure and thus, is utilised extensively in industrial settings to measure both small and large pressures.

2. What are Barometers?

The instruments used to measure atmospheric pressure are known as barometres. The most common and widely used type of barometer is the cistern-type Fortin’s Barometer. Another handy type is the aneroid barometer which does not use any liquid inside it.

3. A bike tire measures a gauge pressure of 35 psi. Find the Absolute Pressure.

Given that,

4. Football shoes have studs on them. Does the concept of pressure play a role here?

Studs have smaller surface areas and thus, exert higher pressure, allowing them to sink into the ground and provide a better grip.

5. What is Atmospheric Pressure?

Ans: Pressure exerted by the atmosphere is known as atmospheric pressure and it is present everywhere on Earth. Its value decreases as we go higher up.

Introduction

A plane slanted at a particular angle is known as an inclined plane. Such a plane is connected to the ground on one end while the other end is raised by a given height that is referred to as the slant height. 

The angle of inclination for an inclined plane is defined as that angle at which an object just starts to slide down due to its own weight.

Inclined plane AB

Body on an inclined plane

Normal force in inclined planes

Generally, it is observed that the normal reaction due to gravitational forces acts just opposite to the weight of the body, especially when placed on the ground. However, that is not universally true. In fact, the normal reaction in the case of an inclined plane acts in a direction that is perpendicular to the incline, not the ground.

Frictional force

Friction occurs when two surfaces come into contact and its tendency is to resist motion. Thus, it always acts opposite to the direction of motion of an object. For an object sliding down an inclined plane, frictional force acts up the incline and vice versa.

Gravitational force components

The gravitational force may be resolved into two components when dealing with an inclined plane. 

1. The normal/vertical part acts perpendicularly to the incline and downwards from it. In the diagram below, it is represented as \({W_{V}}\).
2. Similarly, there exists a horizontal component of the body’s weight that acts parallel to the incline and points downwards. It is represented by \({W_{H}}\)in the diagram.

Resolution of gravitational force

The body is at equilibrium

In the diagram,

N= normal force

W= weight of the body (gravitational force)

\({W_{H}}\)=Horizontal component of the gravitational force

\({W_{V}}\)= Vertical component of the gravitational force

f= frictional force

And we are given that the body is at equilibrium. In such a case,

Body in equilibrium at incline

We can equate the horizontal and vertical forces. Let us start with the horizontal ones:

The quantity μ is known as the coefficient of friction.

Equilibrium of a body on an incline plane:

Two limiting cases of equilibrium exist on an inclined plane:

1. The body is moving up the incline or,
2. It is falling down the incline.

A body moving down the incline.

When the body moves down the incline, we have

N= normal force

W= weight of the body (gravitational force)

\({W_{H}}\)=Horizontal component of the gravitational force

\({W_{V}}\)= Vertical component of the gravitational force

f= frictional force

F= external force

Applying the conditions of equilibrium,

A body moving down the incline.

As before,

N= normal force

W= weight of the body (gravitational force)

\({W_{H}}\)=Horizontal component of the gravitational force

\({W_{V}}\)= Vertical component of the gravitational force

f= frictional force

F=external force

We proceed just as in the previous example.

Solved problems on inclined plane

1. If a block kept on an inclined plane will start slipping, find the angle of inclination given that the coefficient of static friction = 1.73.

We are given the value of = 1.73. We can use the fact that

2. If a block of mass 10 kg remains at rest on an incline of\({45^{0}}\), find the force of friction. (Take\(g=10 m{s^{ – 1}}\))

Given that, the block is at rest so that net force parallel to the incline is zero.

Summary

An inclined plane is a sloping surface designed to move heavy machinery and tools that cannot be lifted directly. Various types of inclined surfaces such as ramps, stairs, and slides exist. 

The primary benefit of an inclined plane is that it helps us move large objects by applying a lesser amount of force. The angle of inclination plays a critical role in determining how much force we must apply and if we would be able to move the object in question at all. For the object to not fall down back on us, we must move it up the incline at a certain angle of friction.

Frequently Asked Questions

1. How many components of gravitational force do we have on an inclined plane?

There are two components we can resolve the gravitational force into:

1. Horizontal component and,
2. Vertical component.

2. Write down two functions of an inclined plane?

Inclined plane has a large number of uses, with the primary ones being,

1. They function as simple machines.
2. They help us move heavy objects upward with ease.

3. What are the forces experienced by an object moving on an inclined plane?

The object experiences gravitational force, normal reaction, and frictional force.

4. In what direction do frictional forces act?

Frictional forces always act opposite the direction of motion of an object.

5. What is the angle of inclination?

It is that angle at which, when a body is placed on an inclined plane, it will start sliding down due to its own weight.

Introduction

A wave is defined as the propagation of a continuous disturbance across two points. They can propagate with, or without a medium in between the given points and on this basis, they are broadly classified as follows:

1. Mechanical waves: A wave that requires a medium to propagate. For sound waves cannot travel in vacuum.
2. Electromagnetic waves: These waves need no medium to travel and thus, can travel in vacuum as well. Light is a common example of electromagnetic waves. They can also be defined as a pulse of energy that traverses through vacuum or a given medium.

Waves generally travel in the form of crests and troughs and are characterised by  various factors like amplitude, velocity, frequency, etc. In simple terms, the amplitude is a measure of the energy they carry. 

Define the Amplitude of a wave

The amplitude of a wave is a measure of the energy transferred by it and is defined as the distance from the axis to the bottom or top of a peak or valley of the wave. Generally, this value is expressed in metres (m), though other measurements exist as well.  Amplitude determines how much the wave rises and falls and waves with higher amplitudes carry more energy than those with lower ones. 

Mathematically, a sinusoidal wave can be represented by the following equation:

We can define amplitude in another way. It can be understood that the amount of displacement of a particle in the wave is an indication of the energy required to create its motion. This quantity of energy is expressed as the amplitude of the wave.

Sound

Sound is a form of energy that causes objects to vibrate. It can be transferred across two locations through a medium that may be solid, liquid, or gas.  Sound waves are longitudinal in nature and thus, move in the form of compressions and rarefactions. When an object produces sound, its vibrations transfer energy to the molecules of the medium around it, which then propagate and reach our eardrums. Our ears convert these vibrations into signals that our brain can interpret as sound.  The range of sound frequencies audible to humans is 20Hz to 20KHz, and frequencies above and below this range are known as ultrasound and infrasound, respectively. 

Ultrasound waves

Ultrasonic waves mostly find use in the medical field in the diagnosis of various diseases. Processes like ultrasonography utilize ultrasounds.

Infrasonic waves

These are sound waves with frequencies below the 20 Hz mark, which are generally produced in natural phenomenon like volcanic eruptions, earthquakes, etc.

Define Amplitude in Physics?

In physics, amplitude refers to the maximum distance or displacement travelled by a vibrating body or wave from its resting point. All waves possess an amplitude and it is an important characteristic that defines waves. 

Amplitude modulation is a technique used to modulate the amplitude of a given wave.  Generally, a low amplitude wave is modulated using a carrier wave. This process allows us to transmit data across locations. Amplitude modulation has several applications such as signal transmission, radio broadcasting among others.

Characteristics of Sound

• Pitch: Pitch refers to the subjective sensation of the frequency of a sound wave. A high-frequency sound wave produces a high pitched sound, while a low-frequency sound wave produces a low pitched sound. Pitch or frequency is measured in Hertz (Hz).
• Loudness: The loudness of sound is determined by the amplitude or size of the sound wave. A larger size or amplitude corresponds to a louder sound. Loudness is measured in decibels (dB).
• Amplitude: Amplitude is the maximum displacement of the particles from their mean position as sound waves travel through the medium. It is expressed in metres.
• Wavelength: Sound is a longitudinal wave and it travels across two points via a medium in the form of compressions and rarefactions. It is characterised by a certain wavelength, which is defined as the distance between two consecutive compressions or rarefactions. Typically, these wavelengths lie between 1.7 cm to 17 metres. 

Wavelength is connected to speed and frequency of sound via the following relation:

  \[\lambda  = \frac{v}{f}\]

• Frequency: The number of compressions or rarefactions that a sound wave produces in unit time is known as the frequency of the wave. It is expressed in Hertz (Hz), which is equal to one second inverse.

  \[f = \frac{1}{T}\]   

• Time period: The time taken for the particles of the medium to undergo a complete cycle from one compression to the next is known as the time period. Time period and frequency are inversely related. Its unit is second.

\[T = \frac{1}{f}\] 

• Velocity: The velocity of the wave measures how fast the disturbance in the medium travels between two locations. It can vary depending on the medium in question and is expressed in (\(m{s^{ – 1}}\))

  Velocity=Displacement/ time

Summary

Waves are a common phenomenon that we encounter in our day-to-day lives. For instaande , the light waves produced by the sun, the waves in the ocean, and the sound waves we hear. In terms of physics, waves are a way of transferring energy via a disturbance. 

Sound waves are generated by a vibrating body that transfers energy to the molecules of the medium that surrounds it. This energy in the form of vibration then propagates through the medium. Sounds can take many forms, such as pleasant sounds, noise, music, etc. Understanding the characteristic properties of sound waves is essential for the creation of music and for other applications.

 

Frequently Asked Questions

1. State the differences between pitch and loudness?

2. Are pitch and frequency different?

Frequency is a measure of how often a particular event occurs whereas pitch is a concept that is closely related to frequency. Even though the two properties are related, there is no mathematical relation for the same. 

Note that while frequency is relevant for all types of waves, including mechanical and electromagnetic waves, the pitch is a challenging concept to define and is relevant only for sound waves.

3. What is the hearing range of the human ear?

Sound waves in the 20 Hz to 20,000 Hz regime are audible to the human ear. It might be interesting to note that while some newborns can hear slightly above the 20 kHz mark, but they lose this sensitivity with age.

4. What is the relation between wavelength, velocity, and frequency of a wave?

\[v = f\lambda \]

From the above relation, it is evident that wavelength and frequency are inversely related. Note that the frequency of a wave never changes. The velocity and wavelength increase or decrease in different media.

5. What are the three ways in which the above equation can be written?

Introduction

In 1820, Hans Oersted conducted a famous experiment using a compass needle and a current-carrying conductor. He observed that when no current was flowing through the conductor placed near the compass, the latter would always point towards the north pole. However, when the conductor was carrying a current, the needle deflected in a particular direction.

He found that the direction of deflection was tangent to a circle, which suggested that current-carrying wires produce a magnetic field around them (Figure 1). This magnetic field due to a urrent-carrying conductor can be calculated using the Biot-Savart law.

To estimate the magnetic field due to a current element, one can first calculate the differential field \(d\overrightarrow B \) and then integrate it over the loop. However, if we have a symmetry in the system, our calculations can be simplified using Ampere’s law.

Who Was André-Marie Ampere?

André-Marie Ampère, a French physicist and mathematician, displayed prodigious talents and began his study of mathematics at the early age of 12. His interest in the field of electromagnetism was sparked by Oersted’s discovery that electric currents produce magnetic fields.

Ampère expanded on Oersted’s work and demonstrated that current-carrying wires either repel or attract one another, depending on whether they were carrying current in the same or in opposite directions. One of his most significant contributions to the field is known as “Ampere’s Law” and in honor of his work, the SI unit of electric current is named after him.

Statement of Ampere’s Circuital law

Ampere’s law can be stated as follows: “The line integral of the magnetic field around any closed loop is proportional to the current passing through the loop.” If there are multiple currents passing through the loop, the algebraic sum of these currents must be taken into account and the loop considered for the calculation is called an “Amperian loop” or “Amperian coil.”

Note that the choice of the loop is aribtary and depends upon our ease of calculation.

Mathematical Form of Ampere’s Circuital Law

If we are given that a current  is flowing through a given loop C, th

\[\oint {\vec B}  \cdot \overrightarrow {dl}  = {\mu _0}{i_{enc}}\]

Line Integral of \(\overrightarrow B \) – The entire current loop can be divided into infinitesimally small subelements \(d\overrightarrow l \) . To calculate the total contribution, we simply integrate the tangential component of \(\overrightarrow B \)  across the length of the loop.

Net current \({i_{enc}}\) – This is the current that is enclosed by the loop. Note that only those currents need to be taken into account which are inside the area of the loop.

From figure  \({i_{enc}} = {i_1} + {i_2}\) only

Ampere’s circuital law

Direction of Integral – We can calculate the direction of the current and magnetic field using the right hand rule. If we curl our right hand such that our thumb points in the positive direction of current, our fingers will then point along the direction of magnetic field.

Inconsistency of Ampere’s Circuital Law

Take a look at the figure below and try to apply Ampere’s law to it. The circuit consists of a capacitor in a circuit wherein, a current \({i_c}\) is flowing. 

Ampere’s circuital isn’t always valid.

Let us take two surfaces 

1. \({S_1}\): A simple circular loop wherein, \({i_{enc}}\)  is simply \({i_{c}}\).
2. The surface \({S_2}\)which is bulged out to the right. Since no current can flow in the gap of the capacitor, \({i_{enc}} = 0\).

Thus, we arrive at a discrepancy wherein, the line integral of magnetic field is both zero and non-zero.

Modified Ampere’s Circuital Law or Ampere – Maxwell’s Circuital Law

Maxwell modified Ampere’s law to remove the aforementioned discrepancy by introducing a term known as the displacement current. It is defined as:

                                 

Where E is the electric field passing through the loop. Notice how this term vanishes when the electric field is constant in time, leading us back to the original Ampere’s law. The modified form thus becomes

                               

And the capacitor problem from before can now be solved:

Correction to Ampere’s law

This time, we notice that inside a capacitor, an electric field exists which varies in time and thus, the discrepancy has now been resolved.

Application of Ampere’s Circuital Law

There are a plethora of situations wherein, Ampere’s law comes in handy. As the first take example, let us calculate magnetic field due to a long wire at a distance r (r >> R)

The magnetic field due to current-carrying wire.

The wire has cylindrical symmetry and we create a circular Amperian loop. Using the right hand rule, the direction of magnetic field comes out to be tangential to every point on the loop and thus,

Ampere’s Law then states that

$$
\begin{gathered}
\oint \vec{B} \cdot \overrightarrow{d l}=\oint B d l=B \oint d l=B \cdot 2 \pi r=\mu_0 I \\
B=\frac{\mu_0{ }^i}{2 \pi r}
\end{gathered}
$$ 

This well-known result can also be verified via Biot-Savart law.

Solved Examples

Example 1. $$
\text {  Find the value for } \vec{B} \cdot \overrightarrow{d l} \text { in surface } 1 \text { and } 2 \text { in units of } \mu_{0^{\circ}}
$$

Ans: Loop S1 contains two currents of values 1A and 5A. Thus,

$$
\vec{B} \cdot \overrightarrow{d l}=6
$$

Similarly, S2 has two currents, but one of them is in the negative direction. Therefore,

$$
\vec{B} \cdot \overrightarrow{d l}=5-2=3
$$

Example 2: A long straight wire of 2cm radius carries a current of 10A. Find the magnetic field at a distance of 8cm from it.

Ans: Using the equation previously derived,

$$
B=\frac{\mu_0{ }^2}{2 \pi r}=\frac{4 \Pi \times 10^7 \times 10}{2 \pi  \times 8 \times 10^{-2}}=\frac{20 \times 10^{-3}}{8}=2.5 \times 10^{-5} \text { Tesla }
$$

Summary

Ampere’s law is a useful tool for estimating the magnetic field due to current distributions when the system exhibits some degree of symmetry. When time varying electric fields are present inside the loop, Ampere’s law fails to produce reasonable results. To address this limitation, Maxwell introduced the concept of Displacement current and a simple demonstration can be made using a capacitor. 

Ampere’s law is particularly useful in estimating the magnetic field due to linear current carrying wires, where the magnitude of the field is inversely proportional to the distance at which it is being calculated.

Frequently Asked Questions 

1. Apart from current carrying wires, what other sources can produce magnetic fields?

Time varying electric fields can produce magnetic fields.

2. Is ampere’s law universally true?

No. The law fails for dynamic cases and is only valid when no time-dependence exists.

3. Is it possible to derive Biot-Savart law from Ampere’s law?

Ampere’s law itself was derived using Biot-Savart law and thus, it is possible to interchange between the two.

4. For the case of electrostatics, is there a law equivalent to Ampere’s law?

Yes, Gauss’ law is almost congruent to Ampere’s law in electrostatics.

5. Summarize Ampere-Maxwell’s law?

Ampere Maxwell’s law proves how a changing electric field can produce a magnetic field, just as a changing magnetic field can induce an electric field (Faraday’s law).

Introduction

The Ampere is one of the seven fundamental units, which include metre, kilogram, second, Kelvin, mole, and Candela. It is used to measure the flow of electric current and is abbreviated as A or amp. Different systems of units like KGS, CGS, and International SI use different units for current and other basic quantities, and conversions can be made between these units. 

An ammeter is a device that measures electric current in amps flowing through a circuit.

What is Ampere?

Ampere, named after Andre-Marie Ampere, is a unit used to measure electric current. It is abbreviated as amp or A. Ampere was a French physicist and mathematician and is considered the father of electromagnetism. 

Initially, the unit Ampere was defined as an electric current equivalent to the flow of  \({10^{19}}\) elementary charges in 1.602176634 seconds. Later, the unit of charge was defined as the coulomb, and Ampere was defined as the flow of one coulomb of charge per second.

1A = 1 C \({\sec ^{ – 1}}\)

A – Ampere (unit of current)

C – Coulomb (unit of charge)

s – second (unit of time)

In the CGS system, the unit of electric current is the “statampere,” which is approximately equal to 10-10 A, while in the International System of Units (SI), one Ampere is defined as the flow of one coulomb of charge per second.

Prefixes of Ampere

To reduce the number of zeros in numerical equivalences, multiples and submultiples of units can be used. These are commonly expressed using prefixes and we list a few here. 

The most common of these are A, kA, MA, mA, and μA and conversion between these sub units is easy.

Ampere Conversion Table

Conversion of Ampere into milliampere

Conversion of Ampere into microampere

Conversion of Ampere into kiloampere

Conversion of Ampere into Megaampere 

Conversion of Watt, Volt, and Ohm into Ampere 

Conversion of Watt into Ampere 

Unlike Ampere, Watt is a unit of power and we can calculate power from current as follows:

Without knowing voltage or resistance, power cannot be calculated solely from the current. For instance, for a device consuming 3000W of power at 100V, the current is:

Conversion of volt into Ampere 

Once again, Volt is a unit of voltage, not current. We can calculate voltage from current given either the power or the resistance. Here is an example. For a 400W devices operating at 20V, the current is:

Conversion of ohm into Ampere 

Ohm measures resistance and Ohm’s law states that

Ammeter

An ammeter is an electronic device designed to measure the flow of electric current in a circuit, which is usually measured in amperes and thus, the name ammeter is given to them. To measure the current, ammeters are connected in series with the circuit and owing to their low resistance, they do not experience significant voltage while performing the measurement. 

Ammeters are available in different ranges, with some used to measure smaller currents in the milliampere (mA) or even the microampere (μA) range. They can be designed to measure both AC as well as DC current.

Types of Ammeter

Ammeters are classified as below

1. Moving coil ammeter
2. Electrodynamic ammeter
3. Moving iron ammeter
4. Digital ammeter
5. Hotwire ammeter
6. Integration ammeter

1. Moving coil ammeter 

A moving coil ammeter is a type of ammeter that can measure both AC and DC current using magnetic deflection. As implied by the name, the coil in this ammeter rotates freely between permanent magnets, owing to the interaction between the current passing through the coil and the magnetic field across it. The current flowing through the circuit is denoted by a pointer connected to this coil.

2. Electrodynamic ammeter 

This ammeter can also measure AC and DC current with an accuracy of 0.10% to 0.25%. The field produced by a fixed coil is used to rotate another coil here, which can denote the value of current. 

3. Moving iron ammeter 

This type of ammeter can also work on both AC and DC. Here, a specially prepared soft iron moves freely between the poles of a permanent magnet or electromagnet. It can be further classified into repulsion or attraction type.

4. Digital ammeter 

A digital ammeter displays the exact value of the current on a digital display. To measure the current, a shunt resistor is added in series with the circuit, and the voltage across the shunt is calibrated to correspond to the current. The voltage is then converted to a digital signal using an analog-to-digital converter and displayed on the screen.

5. Hot wire ammeter 

The heat produced across the wire causes it to expand, which can measure the value of AC or DC current across the circuit.

Summary

The ampere is the standard SI unit of electric current, and is defined as the flow of electric charge in an electric circuit. An ammeter is an instrument used to measure the flow of current in a circuit, and can measure current in a wide variety of subunits like milliamperes, microamperes, and nanoamperes. Ammeters can work in AC and DC circuits.

Current measured in amperes can be converted into milliamperes, microamperes, and nanoamperes, and one can calculate the power and resistance in circuits given two of the three quantities (voltage, current, resistance). Various types of ammeters, such as moving coil ammeters and digital ammeters, are available to measure current in different scenarios.

 

Frequently Asked Questions

1. What does Ampere denote?

André-Marie Ampère, a French physicist and mathematician, is considered the father of electromagnetism and the unit of current, ampere (amp), was named after him. One ampere is defined as the flow of one coulomb of charge per second.

1A = 1C / 1s

2. List two advantages of digital Ammeters over analog ones.

Given below are two advantages of a digital ammeter.

1. Digital ammeters can even work with a small power supply and their accuracy is very high.
2. They are reliable, economical, and last a longer period of time.

3. Why is the connection of the ammeter necessarily in series? What would happen if we connected it in parallel?

An ammeter is a device that measures the current flowing in a circuit, typically measured in amperes. To accurately measure the current, the ammeter must be connected in series with the circuit components. 

Connecting an ammeter in parallel would result in a drastic increase in current since the resistance is very low, which can generate excess heat and potentially harm the device.

4. Discuss the working of a moving coil ammeter?

A moving coil ammeter is one of the various types of ammeter that can measure both AC and DC current. It uses magnetic deflection, with a coil that rotates freely between permanent magnets. The interaction of magnetic field produced with the magnetic field of the magnets causes a deflection in the coil, which can denote current flow.

5. How to convert a moving coil galvanometer into an ammeter?

A moving coil galvanometer can be converted into an ammeter by connecting a low resistance in parallel with it.

Introduction

The term “food chemistry” is used to describe the study of the chemical reactions that take place in the preparation and consumption of food. The composition and functional qualities of foods and food products at different stages are the primary areas of study. While food supplies important elements such proteins, carbs, fats, vitamins, lipids, and minerals. The right nutrients should be included in the diet. Plants and animals are both examples of sources that can be used to create food. Because of the biochemical process it triggers in the body, this food is a rich source of fuel. Sugar, a simple type of carbohydrates, is converted into energy during respiration. Response as follows:

Enzymes and preservatives like flavours, food additives, and colours are also found in food. Manufacturers add preservatives and create new food variations to extend the shelf life of these products. Preservatives extend the shelf life of food without adding any nutritional value, similar to how milk is transformed by fermentation or enzymatic action into curd and cheese. Because of this, food science and chemistry have a positive effect on a wide range of aspects, including:

• Techniques for enhancing food’s shelf-life and avoiding the activity of microbes. 
• Methods for food processing and avoiding food deterioration. 
• Most importantly, food safety and quality enhancer methods.

What is Food Chemistry?

It alludes to the chemical composition of the meal and all of the interactions it has with the body and the environment. Chemical composition, how it is altered by cooking, and how it reacts with the human body are all topics covered. Proteins, carbs, and lipids can all be found in their purest forms in biological items like milk, meat, lettuce, poultry, and so on. Hence, food chemistry is concerned with all modifications made to foods and the improvement of their quality through various methods of food processing.

Chemical in Food

What do Food Chemists do?

A good food chemist should know the science behind food and its application. 

1. He should be able to develop improved food and beverages. 
2. He should be able to analyse methods like canning, heat processing, freezing, and packaging. 
3. He must be aware of the effects of processing on the taste, appearance, freshness, aroma, and vitamin and mineral content of food.

Components of Food

The main component is the necessary diet that is required in a large amount by the body. 

Different Chemicals in Food

The other components or chemicals of food help in various functions of the body and their small quantities are enough.

Other chemicals listed below as preservatives added to food are unhealthy.

Food Components Can Be Broadly Differentiated Into Two Categories.

The food components are divided into two categories: Macronutrients and Micronutrients.

Summary

To learn about the science behind the components of food and their qualities, one must study food chemistry, a large field. It goes through every conceivable structural and molecular shift. A food chemist can oversee these modifications to ensure they don’t compromise the food’s safety or nutritional value in any way. In order for the body to develop and function normally, it need a diet that is both varied and complete.

Frequently Asked Questions

1. Why are preservatives bad for food?

Ans: Some chemicals (present in preservatives) can cause toxic effects like kidney damage, liver disease, DNA damage or impairment of the nervous system, and gastrointestinal symptoms. 

2. What is an alternative for no chemical food?

Ans: Organic food is an alternative, since it has no chemicals  like pesticides or artificial fertilisers. 

3. Why does organic foods spoil faster?

Ans: Organic food is healthy as they are not treated with preservatives or waxes. Therefore, due to the absence of chemicals or preservatives, the shelf life of food decreases and spoils the food at a faster rate. 

Introduction

What happens to a food’s composition, chemistry, and physics while it’s prepared for storage and later consumed is the focus of food chemistry. Recent decades have seen significant expansion in the field of food chemistry. The science of food chemistry investigates the chemical and physical changes that occur in food over time.

The study of compounds used for food preservation through additives is also a part of this field of study. Maleic acid was initially extracted from apples by scientist Carl Wilhelm Scheele in the early 17th century. Then, for ages, scientists have explored food chemistry, searching for new additives and preservatives to boost food quality.

What is Food Chemistry?

The study of foods and their non-living and living constituents is the focus of food chemistry, a scientific discipline in the field of food science. Carbohydrates, lipids, proteins, flavouring compounds, food additives, etc. are all areas where it crosses with biochemistry.

In addition to fats, proteins, and carbs, water is a crucial aspect of every balanced diet.

It discusses the components of food in terms of their content, structure, and physical and chemical qualities. 

In 1950, numerous scientists sought to uncover the root of food additives to combat food contamination. Chemical and physical thermodynamics, quantum mechanics, biopolymer science, colloidal interaction, etc. all contribute to the overarching concept of food chemistry.

Examples of Food Chemistry

Food chemistry is seen in day to day life. Some of the examples are:

• The fermentation of milk, or the creation of curd, and the use of lemon juice to keep apples from browning provide useful analogies.
• In order to determine whether or not a food is safe to eat, food chemists analyse its chemical components. It extends the shelf life of food and is utilised in the preservation process.
• Natural chemicals and enzymes are employed extensively in the food industry to create novel products, such as yeast’s application in baking and lactobacillus’ application in the production of curd from milk.
• Sodium nitrate and vinegar (acetic acid) are just two of the many substances found to extend the shelf life of pickles and other foods.
• Preservatives and other food additives are used to extend the shelf life of fruit juices.

Components of Food

Water is the primary component of most of the foods we eat, however the amount varies widely. Carbohydrates, fats, and proteins are also important parts of a balanced diet. Minerals, vitamins, enzymes, etc., are examples of foods’ ancillary components.

Water: 

Depending on the cuisine, the amount of water in it might range between 40-95%. In the processes of emulsification, freezing, baking, and gel formation, water plays a critical role.

Proteins: 

Amino acids form complicated proteins. These amino acids rebuild bones, muscles, and skin. 50% of a live cell weighs these. It’s required for body growth, hence food contains it. Legumes, grains, beans, peanuts, meat, fish, milk products, and soya milk contain it. Carbon, hydrogen, nitrogen, and oxygen comprise a protein molecule. Food sources provide eight important amino acids. Leucine, valine, tryptophan, tyrosine, lysine, methionine, isoleucine, and phenylalanine.

Carbohydrate: 

Carbohydrates are organic compounds found in many food components like sugar, starch, dextrins, Celluloses, pectins, etc. These are the main source of energy. The carbohydrates are of three types:

1. Monosaccharides,: Glucose, Fructose
2. Disaccharides: Sucrose
3. Polysaccharides: Starch, Glycogen, Cellulose, etc, 

Lipids: 

Food contains oils, fatty acids, and steroids from grains, animal fats, milk products, soybeans, meat, waxes, etc. These are water-insoluble, non-polar dietary compounds that boost energy. Cell membranes need it to store energy.

Vitamins: 

Vitamins are required in a very small amount in our body. These are essential for various metabolic activities of the body. Examples of vitamins are: 

1. Water-Soluble: Vitamin-B (Thiamine, Riboflavin, Niacin, Biotin, Pantothenic Acid, Folic Acid), and Vitamin-C (Ascorbic acid).
2. Fat-Soluble: Vitamin-A, Vitamin-D, Vitamin-E, And Vitamin-K.

Minerals: 

Minerals are also crucial to our health and are found in many different foods. Excessive use can be harmful to health, thus only a modest amount is needed. Calcium, magnesium, potassium, copper, iron, and zinc are all examples of minerals that play an important role in human health.

Structure 

Let’s understand food components by their structure.

Carbohydrates: A single carbohydrate molecule is calles a monosaccharide, while two or more carbohydrate molecules are called disaccharide and polysaccharide. 

Carbohydrates

Proteins: Proteins are the chain of amino acids bonded by the peptide bond between the amino group and the carboxylic group. 

Lipids: Lipids are of two types saturated and unsaturated fatty acids. Triglycerides are formed by one molecule of glycerol and three molecules of fatty acids. In the reaction, the R, R’, R” are the chains of 10 to 20 carbon. 

Summary 

Food chemistry is the study of the chemical and physical modifications made to foods and their constituents. Additives, preservatives, flavouring agents, enzymes, minerals, and vitamins are now included included in the field of food science. Carbohydrates make up a sizable portion of the food we eat.

Some of the most important vitamins for our bodies are carried by lipids, which are present in oil cereals, meat, milk, and dairy products.

Frequently Asked Questions 

1. How is a mixture of oil and water stabilized in food chemistry?

Ans. Emulsifiers are the chemical components used for mixing two food containing oil and water. One of the natural emulsifiers is Lecithin found in egg yolk and plant tissues which are used to make mayonnaise and salad dressings. 

2. What is the importance of phosphorus?

Ans. Phosphorus is an important macro mineral in our body, it is found in many foods like fats from animal meat, fish, egg, and milk. It is important for DNA and RNa production.

3. What is aromatic food?

Ans. Aromatics are vegetables, herbs, and spices that add aroma and flavor to dishes. They consist of mainly phenols.

Introduction

Mankind has only recently begun to utilise fluorine. Materials containing fluorine were infrequently used in antiquity. Smelting fluorite was an economic focus for Georgius Agricola, who investigated its application in the 16th century. Both the word “fluorite” and “fluorine” were created by Agricola. In the later part of the 18th century, hydrofluoric acid was uncovered. Much like chlorine, fluorine was discovered to be bound in compounds in the nineteenth century. Calcium fluoride, or fluorite, is a mineral that can be discovered. Fluorine is difficult to separate because of its strong bonds and the toxicity of hydrogen fluoride. Electrolysis of potassium fluoride and hydrogen fluoride produced elemental fluorine in 1886, and the discovery was made by French chemist and Nobel laureate Henri Moissan. During World War 2, massive amounts of fluorine were produced and utilised by the Manhattan Project. Polytetrafluoroethylene (Teflon) plastic and refrigerant gases were both developed by DuPont this century (Freon).

What is Fluorine?

Gaseous halogen the element fluorine can be found in the 17th group of the periodic chart. The element has an atomic number of 9. One of fluorine’s defining characteristics is that it is the most electronegative element in the periodic table. Under normal conditions, it presents as a pale yellow diatomic gas that is highly toxic. At 3.98 on the Pauling scale, fluorine has the highest electronegativity of any element.

Electron Configuration And Chemical Properties of Fluorine

The gas fluorine, which belongs to the 17th group, has an atomic number of 9. The halogen nature of fluorine gives it a valency of one. Due to its one electron deficit, it accepts electrons from other substances. They accept electrons, making these compounds oxidising agents. Don’t forget that electron donors always act as reducing agents and electron acceptors as oxidising ones. Because of its high electronegativity, fluorine is the most powerful oxidising agent among the halogens. An electrical configuration of 1s22s22p5 describes fluorine.

Fluorine 

Properties of Fluorine

Fluorine shows different physical and chemical properties. 

Chemical Properties of Fluorine

• Fluorine is one of the most powerful oxidising agents since it is a strongly electronegative element. According to the Pauling scale, fluorine has an electronegativity of 3.98.
•  The strong force of attraction between the nucleus and the electrons caused by their small size results in a very high energy requirement to extract an electron. Fluorine has an initial ionisation energy of 1680.6 KJ/Mol. Thus, it takes 1680.6 KJ of energy to remove an electron from a mole of fluorine. 
• Fluorine has a standard potential of 2.87 V. Compared to all other factors, this is the highest. 
• There is only one stable isotope of fluorine, which is fluorine 19.

Physical properties of Fluorine

• Fluorine is the lightest of all the halogens, with an estimated atomic mass of 19 particles. 
• In its natural state, fluorine can be found as a gas. It is a light gas with a pale-yellow colour. 
• Fluorine has a boiling point of -188° C and a melting point of 219.6° C.

The Atomic Radius of Fluorine

The atomic radius of fluorine, a very small element, is extremely small. A fluorine atom has a very strong nuclear force because of this. The smallest halogen atom is fluorine, which has an atomic radius of only 147 pm.

What is the Atomic Mass of Fluorine?

The lightest halogen gas, fluorine, weighs only 19 amu; specifically, it is 18.99 amu. Conventionally, we round it off and count it as 19.

Fun Facts About Fluorine

• In the crust of the earth, fluorine is the 13th most abundant element.
• Fluorine is a very reactive element that is never discovered in its pure form. It is always present in some combination with another element.
• Water can be burned by fluorine with a brilliant blaze.
• Fluorine can also be found in the earth’s crust in addition to the air. Coal and other elements contain fluorine in trace amounts. 
• Fluorine is nearly non-existent in the air. 50 parts per billion roughly. Before the Second World War, fluorine was not well recognised in the business.
• Fluorine hadn’t been produced commercially until that point. Everyone just understood fluorine as an element that can combine to form salts. Uranium hexafluoride, however, was discovered to have nuclear capabilities and be a source of energy during World War 2. Fluorine has since been produced industrially at an exponential rate. 
• Animals require ion fluoride, which helps to strengthen their teeth and bones. In some places, it is added to drinking water. 

Summary

Fluorine is one of the halogen family members in the periodic table. Fluorine exists as yellow gas having an unpleasant smell when it is at room temperature. It is harmful to breathe in the gas. Fluorine becomes a yellow liquid when it cools. Fluorine-19 is the only stable isotope of the substance. The most significant source of fluorine is fluorspar.

 

Frequently Asked Questions

1. What are the principle sources of Fluorine?

Ans: The principal source mineral, fluorite, was originally reported in 1529 by Georgius Agricola, known as the “father of mineralogy,” and the word “fluorine” is derived from this Latin stem. Fluorite, according to him, is an addition known as a flux that aids in melting ores and slags during smelting.

2. Why is Fluorine so important?

Ans: Our bones’ ability to remain firm depends on fluorine. If we use fluoridated toothpaste twice a day, it can also prevent tooth decay. Too much fluorine absorption can affect the kidneys, bones, nerves, and muscles in addition to causing osteoporosis and tooth decay.

3. What are the safety precautions for handling fluorine?

Ans: Use and store fluorine in a ventilated gas cabinet or fume hood. When a gas cabinet is warranted (e.g., cylinders larger than lecture bottle size that are used in a fume hood), install a fluorine gas monitoring system. Follow all applicable recommendations for storage and handling of compressed gases.