Electromagnetic Induction

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Summary

Chapter Six: Electromagnetic Induction

Summary

Electricity and magnetism are inter-related phenomena.
Faraday and Henry demonstrated that electric currents can be induced by changing magnetic fields.
Electromagnetic induction is the process of generating electric current through varying magnetic fields.
Key concepts include:
- Magnetic Flux:
  - Defined as $\Phi_B = B \cdot A = BA \cos(\Theta)$
- Faraday's Law of Induction:
  - The induced emf in a coil is proportional to the rate of change of magnetic flux.
- Lenz's Law:
  - The direction of induced emf opposes the change in magnetic flux.
- Motional EMF:
  - Induced emf when a conductor moves in a magnetic field is given by $\epsilon = B l u$
- Inductance:
  - Defined as the ratio of flux linkage to current, $L = \frac{N \Phi}{I}$
- Mutual Inductance:
  - Induced emf in one coil due to a change in current in another coil is given by $\epsilon_1 = -M_{12} \frac{dI_2}{dt}$
- Self-Inductance:
  - Induced emf in a coil due to its own changing current is given by $\epsilon = -L \frac{dI}{dt}$

Key Formulas and Definitions

Quantity	Symbol	Units	Equations
Magnetic Flux	$\Phi_B$	Wb (weber)	$\Phi_B = B \cdot A$
EMF	$\epsilon$	V (volt)
Mutual Inductance	$M$	H (henry)	$\epsilon_1 = -M_{12} \frac{dI_2}{dt}$
Self Inductance	$L$	H (henry)	$\epsilon = -L \frac{dI}{dt}$

Learning Objectives

Understand the relationship between electricity and magnetism.
Explain the phenomenon of electromagnetic induction.
Describe Faraday's laws of induction and their implications.
Apply Lenz's law to determine the direction of induced current.
Calculate induced emf in various scenarios involving changing magnetic fields.
Define and calculate mutual and self-inductance.
Analyze the operation of AC generators and their principles.

Detailed Notes

Chapter Six: Electromagnetic Induction

6.1 Introduction

Electricity and magnetism were historically viewed as separate phenomena.
Early experiments by Oersted and Ampere established their interrelation.
Moving electric charges produce magnetic fields.
Faraday and Henry's experiments demonstrated that changing magnetic fields can induce electric currents.
This phenomenon is known as electromagnetic induction.

6.2 Key Concepts

Magnetic Flux

Defined as:

$\Phi_B = B \cdot A = BA \cos(\Theta)$
where $\Theta$ is the angle between the magnetic field $B$ and the area $A$ .

Faraday's Laws of Induction

The induced emf in a coil of $N$ turns is related to the rate of change of magnetic flux:

$\epsilon = -N \frac{d\Phi_B}{dt}$
If the circuit is closed, the current $I$ is given by:

$I = \frac{\epsilon}{R}$
where $R$ is the resistance of the circuit.

Lenz's Law

The polarity of the induced emf opposes the change in magnetic flux that produces it.

Induced EMF Formulas

Motional emf for a rod moving in a magnetic field:

$\epsilon = B l u$
where $l$ is the length of the rod and $u$ is its velocity.
Self-inductance:

$\epsilon = -L \frac{dI}{dt}$
where $L$ is the self-inductance of the coil.
Mutual inductance:

$\epsilon_1 = -M_{12} \frac{dI_2}{dt}$
where $M_{12}$ is the mutual inductance.

6.3 Examples

Example 6.3: A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside. If the current changes from 2.0 A to 4.0 A in 0.1 S, calculate the induced emf.
Example 6.4: A rectangular wire loop moving out of a uniform magnetic field of 0.3 T. Calculate the emf developed across a cut in the loop.
Example 6.5: A metallic rod rotated in a magnetic field of 0.5 T. Calculate the emf developed between the center and the ring.

6.4 Important Formulas and Definitions

Quantity	Symbol	Units	Dimensions	Equations
Magnetic Flux	$\Phi_B$	Wb (weber)	[ML²T⁻²A⁻¹]	$\Phi_B = B \cdot A$
EMF	$\epsilon$	V (volt)	[ML²T⁻³A⁻¹]
Mutual Inductance	$M$	H (henry)	[M L²T⁻²A⁻²]	$\epsilon_1 = -M_{12} \frac{dI_2}{dt}$
Self Inductance	$L$	H (henry)	[ML²T⁻²A⁻²]	$\epsilon = -L \frac{dI}{dt}$

6.5 Points to Ponder

The relationship between electricity and magnetism is fundamental.
Induced currents oppose changes in magnetic flux, adhering to conservation of energy principles.
The self-inductance of a solenoid depends on its geometry and the permeability of the core material.

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Misunderstanding Lenz's Law: Students often forget that the induced current opposes the change in magnetic flux. Remember that the negative sign in Faraday's law indicates this opposition.
Confusing Self-Inductance and Mutual Inductance: Be clear about the difference; self-inductance refers to a coil inducing emf in itself, while mutual inductance refers to one coil inducing emf in another.
Neglecting the Direction of Induced Current: When solving problems, always determine the direction of the induced current using Lenz's law to avoid incorrect answers.
Forgetting Units: Ensure that you are using the correct units for magnetic flux (Wb), emf (V), and inductance (H) in calculations.

Exam Tips

Practice with Diagrams: Familiarize yourself with diagrams showing coils and magnetic fields, as visualizing these can help in understanding the concepts of induction.
Work Through Examples: Go through examples like the induced emf in a moving loop or changing current scenarios to solidify your understanding.
Review Key Formulas: Make sure to memorize key formulas such as Faraday's law, Lenz's law, and the equations for self and mutual inductance.
Understand the Concept of Magnetic Flux: Be clear on how to calculate magnetic flux and its relation to area and magnetic field direction.

Practice & Assessment

Multiple Choice Questions

The galvanometer shows a deflection.

The galvanometer shows no deflection.

The galvanometer explodes.

The galvanometer shows a constant reading.

Correct Answer: A

Solution:

When a coil connected to a galvanometer is moved towards a stationary coil connected to a battery, the galvanometer shows a deflection due to the induced current.

\varepsilon = NBA (2\pi V) \sin(2\pi Vt)

\varepsilon = NBA \cos(2\pi Vt)

\varepsilon = NBA (2\pi V) \cos(2\pi Vt)

\varepsilon = NBA \sin(2\pi Vt)

Correct Answer: A

Solution:

The motional emf in an AC generator is given by

\varepsilon = NBA (2\pi V) \sin(2\pi Vt)

, where

t

is time and the coil is initially perpendicular to the field.

L = \mu_r \mu_0 N^2 A l

L = \mu_0 N^2 A l

L = \mu_r \mu_0 N^2 A / l

L = \mu_r \mu_0 N A l

Correct Answer: A

Solution:

The self-inductance

L

of a solenoid is given by the formula

L = \mu_r \mu_0 N^2 A l

, where

\mu_r

is the relative permeability of the core,

\mu_0

is the permeability of free space,

N

is the number of turns per unit length,

A

is the cross-sectional area, and

l

is the length of the solenoid.

A momentary deflection in the galvanometer connected to

C_1

A continuous deflection in the galvanometer connected to

C_1

No deflection in the galvanometer connected to

C_1

A deflection in the galvanometer only when the key is released.

Correct Answer: A

Solution:

When the key is pressed, the current in

C_2

changes, inducing a momentary emf in

C_1

due to the change in magnetic flux, causing a deflection in the galvanometer.

The galvanometer shows a deflection.

The galvanometer shows no deflection.

The galvanometer deflects in the opposite direction.

The galvanometer explodes.

Correct Answer: A

Solution:

The galvanometer shows a deflection when the coil is moved towards a stationary magnet, indicating the induction of electric current.

62.8 V

125.6 V

188.4 V

251.2 V

Correct Answer: B

Solution:

The maximum emf is given by

\varepsilon_{max} = NBA(2\pi f)

, where

N = 100

B = 0.2 \text{ T}

A = 0.1 \text{ m}^2

, and

f = 50 \text{ Hz}

. Substituting these values,

\varepsilon_{max} = 100 \times 0.2 \times 0.1 \times 2\pi \times 50 = 125.6 \text{ V}

To generate magnetic fields

To measure electric current

To store electric charge

To increase resistance

Correct Answer: B

Solution:

A galvanometer is used to detect and measure the presence of electric current in the coil during electromagnetic induction experiments.

To create a momentary change in current.

To maintain a constant current.

To reverse the direction of current.

To increase the resistance in the circuit.

Correct Answer: A

Solution:

The tapping key is used to create a momentary change in current, which induces a current in the nearby coil.

Electric current is generated by varying magnetic fields.

Electric current is generated by static magnetic fields.

Electric current is generated by constant electric fields.

Electric current is generated by static electric charges.

Correct Answer: A

Solution:

Electromagnetic induction refers to the generation of electric current by changing magnetic fields, as discovered by Faraday and Henry.

The induced emf increases.

The induced emf decreases.

The induced emf remains constant.

There is no induced emf.

Correct Answer: A

Solution:

As the loop shrinks, the area enclosed by the loop decreases, leading to a decrease in magnetic flux through the loop. According to Faraday's law, a change in magnetic flux induces an emf, which increases as the rate of change of area increases.

The temperature of the coil

The rate of change of magnetic flux through the coil

The color of the coil

The length of the coil

Correct Answer: B

Solution:

Faraday's law states that the induced emf in a coil is directly related to the rate of change of magnetic flux through it.

The deflection decreases.

The deflection remains the same.

The deflection increases dramatically.

The deflection becomes zero.

Correct Answer: C

Solution:

Inserting an iron rod into the coils increases the deflection dramatically, indicating a stronger induced current.

Electric currents are induced in closed coils when subjected to changing magnetic fields.

Electric currents are induced in open circuits when subjected to constant magnetic fields.

Magnetic fields are generated by stationary electric charges.

Electric currents are induced only when magnets are stationary.

Correct Answer: A

Solution:

Electromagnetic induction occurs when electric currents are induced in closed coils due to changing magnetic fields, as demonstrated by Faraday and Henry.

The galvanometer shows no deflection.

The galvanometer shows a deflection indicating current.

The galvanometer needle breaks.

The galvanometer shows deflection only when the magnet is stationary.

Correct Answer: B

Solution:

When the north pole of a bar magnet is pushed towards the coil, the galvanometer shows a deflection, indicating the presence of an induced current.

A magnet is moved slowly towards a stationary coil.

A magnet is moved quickly towards a stationary coil.

A stationary magnet is placed near a moving coil.

A magnet is rotated at a constant speed near a stationary coil.

Correct Answer: B

Solution:

Faraday's law states that the induced emf is directly proportional to the rate of change of magnetic flux. Moving the magnet quickly increases the rate of change of magnetic flux through the coil, resulting in a higher induced emf.

The induced current will flow in a clockwise direction.

The induced current will flow in a counterclockwise direction.

There will be no induced current as the magnetic field is uniform.

The direction of the induced current cannot be determined with the given information.

Correct Answer: B

Solution:

According to Lenz's law, the induced current will oppose the change in magnetic flux. Since the magnetic field is increasing, the induced current will flow in a direction that creates a magnetic field opposing this increase. Therefore, the current will flow in a counterclockwise direction.

Clockwise, when viewed from the magnet side

Counterclockwise, when viewed from the magnet side

No current is induced

Direction depends on the speed of the magnet

Correct Answer: B

Solution:

Lenz's Law states that the direction of the induced current will be such that it opposes the change in magnetic flux. Thus, if a north pole is approaching the coil, the induced current will create its own north pole facing the magnet, resulting in a counterclockwise current when viewed from the magnet side.

0.12 V

0.24 V

0.48 V

0.60 V

Correct Answer: A

Solution:

The induced emf (ε) can be calculated using Faraday's Law: ε = -N (dΦ/dt), where N is the number of turns in the loop. The change in magnetic flux (dΦ) is given by the change in current times the area of the loop and the number of turns per unit length. Thus, ε = -15 * 0.0002 * (4 - 2) / 0.1 = 0.12 V.

The deflection on the galvanometer increases dramatically.

The deflection on the galvanometer decreases.

There is no change in the deflection on the galvanometer.

The galvanometer shows a constant deflection.

Correct Answer: A

Solution:

Inserting an iron rod into the coils increases the magnetic flux linkage, thereby increasing the induced current and the deflection on the galvanometer.

The coil is generating heat

A current is induced in the coil

The magnet is losing its magnetic properties

The galvanometer is malfunctioning

Correct Answer: B

Solution:

The deflection in the galvanometer indicates that a current is induced in the coil due to the movement of the magnet, demonstrating electromagnetic induction.

Increasing the core's relative permeability

\mu_r

Decreasing the number of turns per unit length

n

Decreasing the area of cross-section

A

Shortening the length

l

of the solenoid.

Correct Answer: A

Solution:

The self-inductance

L

is directly proportional to the relative permeability

\mu_r

. Increasing

\mu_r

will increase

L

, while the other options would decrease it.

The galvanometer shows a deflection.

The galvanometer shows no deflection.

The galvanometer deflects in the opposite direction.

The galvanometer explodes.

Correct Answer: A

Solution:

When the North-pole of a bar magnet is pushed towards the coil, the pointer in the galvanometer deflects, indicating the presence of electric current in the coil.

In the direction of the magnetic field.

Opposite to the change in magnetic flux.

Perpendicular to the magnetic field.

In the same direction as the change in magnetic flux.

Correct Answer: B

Solution:

Lenz's law states that the induced current will flow in a direction that opposes the change in magnetic flux that produces it.

Experiments by Michael Faraday and Joseph Henry

Experiments by Oersted and Ampere

Experiments by Newton and Galileo

Experiments by Tesla and Edison

Correct Answer: A

Solution:

Michael Faraday and Joseph Henry conducted experiments around 1830 that conclusively demonstrated electromagnetic induction, where electric currents were induced in closed coils by changing magnetic fields.

The galvanometer shows a continuous deflection.

The galvanometer shows a momentary deflection.

The galvanometer shows no deflection.

The galvanometer explodes.

Correct Answer: B

Solution:

It is observed that the galvanometer shows a momentary deflection when the tapping key is pressed. The pointer in the galvanometer returns to zero immediately.

4 H

2 H

1 H

0.5 H

Correct Answer: A

Solution:

The self-inductance

L

is given by

\epsilon = -L \frac{\Delta I}{\Delta t}

, where

\epsilon = 200 \text{ V}

\Delta I = 5.0 \text{ A}

, and

\Delta t = 0.1 \text{ s}

. Solving for

L

, we get

L = \frac{200 \times 0.1}{5.0} = 4 \text{ H}

The amount of magnetic field passing through a surface

The speed of light in a vacuum

The gravitational force on an object

The electric charge of an electron

Correct Answer: A

Solution:

Magnetic flux refers to the amount of magnetic field passing through a surface, and it is a key concept in electromagnetic induction.

Isaac Newton

Michael Faraday

Albert Einstein

James Clerk Maxwell

Correct Answer: B

Solution:

Michael Faraday demonstrated that electric currents were induced in closed coils when subjected to changing magnetic fields.

It requires a stationary magnetic field.

It only occurs with direct current.

It involves the generation of electric current by changing magnetic fields.

It cannot occur in a vacuum.

Correct Answer: C

Solution:

Electromagnetic induction involves the generation of electric current by changing magnetic fields, as demonstrated by Faraday's experiments.

\epsilon = Blv

\epsilon = B^2lv

\epsilon = \frac{Blv}{2}

\epsilon = 2Blv

Correct Answer: A

Solution:

The motional emf induced in a conductor moving perpendicular to a magnetic field is given by the expression

\epsilon = Blv

, where

B

is the magnetic field,

l

is the length of the conductor, and

v

is the velocity of the conductor.

The induced current decreases

The induced current remains the same

The induced current increases

The induced current is zero

Correct Answer: C

Solution:

The induced current increases when the relative motion between the coil and the magnet is increased, as the rate of change of magnetic flux through the coil is greater.

Clockwise

Counterclockwise

No current is induced

Cannot be determined

Correct Answer: B

Solution:

According to Lenz's law, the induced current will oppose the change in magnetic flux. As the loop is pulled out, the magnetic flux through the loop decreases. The induced current will be counterclockwise to create a magnetic field into the page, opposing the decrease.

The galvanometer will show a deflection in the opposite direction.

The galvanometer will show no deflection.

The galvanometer will show a deflection in the same direction.

The galvanometer will show a fluctuating deflection.

Correct Answer: A

Solution:

According to Faraday's law of electromagnetic induction, a change in magnetic flux through the coil induces an electromotive force (emf), causing a current. When the magnet is moved away, the change in flux is opposite to when it was moved towards, resulting in a deflection in the opposite direction.

No current is induced in the coil.

A current is induced in the coil in the same direction as when moved towards the magnet.

A current is induced in the coil in the opposite direction.

The coil becomes magnetized permanently.

Correct Answer: C

Solution:

When a coil is moved away from a stationary magnet, a current is induced in the coil in the opposite direction to when it is moved towards the magnet.

Clockwise

Counterclockwise

Alternating

No current is induced

Correct Answer: B

Solution:

Lenz's law states that the direction of induced current is such that it opposes the change in magnetic flux that produces it. As the loop is deformed into a narrow straight wire, the area enclosed by the loop decreases, reducing the magnetic flux through it. To oppose this decrease, the induced current must flow in a direction that increases the magnetic flux, which is counterclockwise when viewed from above.

The galvanometer shows a momentary deflection.

The galvanometer shows a continuous deflection.

The galvanometer shows no deflection.

The galvanometer shows a deflection only when the key is released.

Correct Answer: A

Solution:

Pressing the tapping key causes a momentary deflection in the galvanometer due to the induced current.

Enhances the change in magnetic flux

Opposes the change in magnetic flux

Is random

Is always clockwise

Correct Answer: B

Solution:

Lenz's law states that the polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces it.

It decreases the induced emf.

It has no effect on the induced emf.

It increases the induced emf.

It reverses the direction of the induced current.

Correct Answer: C

Solution:

Inserting an iron rod into a coil increases the induced emf because the iron rod enhances the magnetic field within the coil.

0.024 V

0.048 V

0.006 V

0.012 V

Correct Answer: A

Solution:

The emf induced (ε) is given by ε = B * l * v, where B is the magnetic field, l is the length of the side perpendicular to the velocity, and v is the velocity. Here, B = 0.3 T, l = 0.08 m, v = 0.01 m/s. Thus, ε = 0.3 * 0.08 * 0.01 = 0.024 V.

The induced current will support the motion of the magnet.

The induced current will oppose the motion of the magnet.

The induced current will have no specific direction.

The induced current will enhance the magnetic field.

Correct Answer: B

Solution:

Lenz's law states that the induced current will flow in a direction that opposes the change in magnetic flux that produces it.

The galvanometer shows a steady deflection.

The galvanometer shows a momentary deflection and then returns to zero.

The galvanometer shows no deflection.

The galvanometer shows a deflection as long as the switch is closed.

Correct Answer: B

Solution:

When the switch is closed, the current in Coil 2 changes, inducing a momentary emf in Coil 1 due to the change in magnetic flux. The galvanometer shows a momentary deflection as the flux changes and then returns to zero when the current stabilizes.

\mu_0 n^2 A l

\mu_r \mu_0 n^2 A l

\mu_r n^2 A l

\mu_0 \mu_r n A l

Correct Answer: B

Solution:

The self-inductance

L

of a long solenoid is given by

L = \mu_r \mu_0 n^2 A l

, where

\mu_r

is the relative permeability,

\mu_0

is the permeability of free space,

n

is the number of turns per unit length,

A

is the cross-sectional area, and

l

is the length of the solenoid.

Electromagnetic induction

Thermal conduction

Nuclear fusion

Chemical reaction

Correct Answer: A

Solution:

Modern-day generators operate on the principle of electromagnetic induction, where mechanical energy is converted to electrical energy.

It states that the induced current will enhance the change in magnetic flux.

It states that the induced current will oppose the change in magnetic flux.

It states that the induced current will have no effect on the magnetic flux.

It states that the induced current will double the magnetic flux.

Correct Answer: B

Solution:

Lenz's law states that the polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces it.

0.015 V

0.030 V

0.045 V

0.060 V

Correct Answer: A

Solution:

The induced emf (ε) is calculated using the formula ε = B * l * v, where B is the magnetic field, l is the length of the wire, and v is the velocity. Substituting the given values, ε = 0.30 x 10⁻⁴ * 10 * 5.0 = 0.015 V.

The self-inductance remains the same.

The self-inductance doubles.

The self-inductance quadruples.

The self-inductance halves.

Correct Answer: C

Solution:

The self-inductance

L

of a solenoid is given by

L = \mu_r \mu_0 n^2 A l

, where

n

is the number of turns per unit length. Doubling

n

results in

n^2

becoming four times its original value, thus quadrupling the self-inductance.

The reading decreases

The reading increases

The reading remains unchanged

The reading fluctuates randomly

Correct Answer: B

Solution:

When the North-pole of a bar magnet is pushed towards the coil, the pointer in the galvanometer deflects, indicating the presence of electric current in the coil.

0.2 \text{ V}

0.6 \text{ V}

0.4 \text{ V}

0.1 \text{ V}

Correct Answer: B

Solution:

The motional emf

\varepsilon

is given by

\varepsilon = B l v

. Substituting the given values,

\varepsilon = 0.2 \times 1 \times 3 = 0.6 \text{ V}

The induced emf is directly proportional to the rate of change of magnetic flux.

The induced emf is inversely proportional to the rate of change of magnetic flux.

The induced emf is independent of the rate of change of magnetic flux.

The induced emf is equal to the magnetic flux.

Correct Answer: A

Solution:

Faraday's law states that the induced emf in a coil is directly related to the rate of change of magnetic flux through it.

15 Wb

30 Wb

45 Wb

60 Wb

Correct Answer: B

Solution:

The change of flux linkage (ΔΦ) is given by the product of mutual inductance (M) and the change in current (ΔI). Thus, ΔΦ = M * ΔI = 1.5 H * 20 A = 30 Wb.

It has no practical applications.

It is only useful for academic purposes.

It led to the development of modern generators and transformers.

It is only applicable in theoretical physics.

Correct Answer: C

Solution:

Faraday's discovery of electromagnetic induction has significant practical applications, leading to the development of modern generators and transformers.

ΦB = B + A

ΦB = B - A

ΦB = B \times A

ΦB = B \cdot A \cos \Theta

Correct Answer: D

Solution:

The magnetic flux through a surface of area

A

in a uniform magnetic field

B

is given by

\Phi_B = B \cdot A \cos \Theta

, where

\Theta

is the angle between

B

and

A

A coil moving towards a stationary magnet.

A magnet moving towards a stationary coil.

A coil connected to a battery and a nearby coil connected to a galvanometer.

A stationary coil with a stationary magnet.

Correct Answer: C

Solution:

A coil connected to a battery can create a changing magnetic field, which induces an emf in a nearby coil connected to a galvanometer.

The induced current increases.

The induced current decreases.

The induced current remains constant.

The induced current stops.

Correct Answer: D

Solution:

When the relative motion between the coil and the magnet is stopped, the change in magnetic flux ceases, resulting in no induced current.

Clockwise

Counterclockwise

No current is induced

Cannot be determined

Correct Answer: A

Solution:

As the loop is deformed, the area enclosed by the loop decreases, reducing the magnetic flux through it. According to Lenz's law, the induced current will be clockwise to oppose the decrease in magnetic flux by creating a magnetic field into the page.

\varepsilon = Blv

\varepsilon = Bv/l

\varepsilon = B/lv

\varepsilon = Bv^2l

Correct Answer: A

Solution:

The induced emf (called motional emf) across the ends of the rod is given by

\varepsilon = Blv

The induced current flows in a direction that opposes the change in magnetic flux.

The induced current flows in the same direction as the change in magnetic flux.

The induced current flows in a random direction.

The induced current does not depend on the change in magnetic flux.

Correct Answer: A

Solution:

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produces it.

0.0785 \text{ V}

0.157 \text{ V}

0.314 \text{ V}

0.628 \text{ V}

Correct Answer: C

Solution:

The induced emf

\varepsilon

is given by Faraday's law

\varepsilon = -\frac{d\Phi_B}{dt}

. The magnetic flux

\Phi_B = B \cdot A = B \cdot \pi r^2

. Thus,

\varepsilon = \pi r^2 \cdot \frac{dB}{dt} = \pi (0.5)^2 \cdot 0.1 = 0.314 \text{ V}

The induced emf decreases

The induced emf remains the same

The induced emf increases

The induced emf becomes zero

Correct Answer: C

Solution:

The deflection (and hence current) is found to be larger when the magnet is pushed towards or pulled away from the coil faster.

The magnet will accelerate uniformly due to gravity.

The magnet will experience a constant velocity.

The magnet will decelerate as it falls through the tube.

The magnet will oscillate inside the tube.

Correct Answer: C

Solution:

As the magnet falls through the copper tube, it induces eddy currents in the tube due to the changing magnetic field. These eddy currents create a magnetic field that opposes the motion of the magnet, causing it to decelerate.

An electromotive force (emf) is induced in the coil.

The coil generates a constant magnetic field.

The coil's resistance decreases.

The coil becomes electrically neutral.

Correct Answer: A

Solution:

Faraday's law states that a change in magnetic flux through a coil induces an electromotive force (emf) in the coil.

50 V

100 V

200 V

400 V

Correct Answer: A

Solution:

The emf developed is given by the formula for motional emf:

\varepsilon = \frac{1}{2} B \omega L^2

, where

B = 0.5 \text{ T}

\omega = 400 \text{ rad/s}

, and

L = 1.0 \text{ m}

. Substituting the values, we get

\varepsilon = \frac{1}{2} \times 0.5 \times 400 \times 1.0^2 = 50 \text{ V}

Ohm's Law

Lenz's Law

Faraday's Law of Electromagnetic Induction

Ampere's Circuital Law

Correct Answer: C

Solution:

The deflection of the galvanometer needle when the magnet is moved towards the coil is explained by Faraday's Law of Electromagnetic Induction, which states that a change in magnetic flux through a coil induces an electromotive force (emf) in the coil.

The galvanometer shows a deflection only when the magnet is moving towards the coil.

The galvanometer shows a deflection only when the magnet is stationary near the coil.

The galvanometer shows a deflection only when the magnet is moving away from the coil.

The galvanometer shows a deflection both when the magnet is moving towards and away from the coil.

Correct Answer: D

Solution:

According to Faraday's experiments, the galvanometer shows a deflection when there is relative motion between the magnet and the coil, indicating an induced current. This happens both when the magnet is moving towards and away from the coil, as the change in magnetic flux induces an emf.

True or False

Correct Answer: False

Solution:

Electromagnetic induction has many practical applications, such as in generators and transformers, and is crucial for modern electrical technology.

Correct Answer: False

Solution:

A changing current in a nearby coil can induce an emf in a stationary coil, not a steady current.

Correct Answer: True

Solution:

Oersted and Ampere's experiments established the relationship between electricity and magnetism, showing that moving electric charges generate magnetic fields.

Correct Answer: True

Solution:

Mutual inductance refers to the phenomenon where a changing current in one coil induces an emf in a nearby coil, as described in electromagnetic induction principles.

Correct Answer: False

Solution:

Faraday's experiments demonstrated that it is the relative motion between a magnet and a coil that induces a current, not a stationary magnet.

Correct Answer: False

Solution:

A stationary coil cannot induce an electric current in another stationary coil without a change in magnetic flux or external influence.

Correct Answer: False

Solution:

Oersted and Ampere's experiments demonstrated that electricity and magnetism are inter-related, as moving electric charges produce magnetic fields.

Correct Answer: False

Solution:

Electromagnetic induction is crucial for modern technology, enabling the operation of generators, transformers, and many other devices.

Correct Answer: False

Solution:

In an AC generator, mechanical energy is converted to electrical energy through electromagnetic induction.

Correct Answer: False

Solution:

Self-inductance is a measure of a coil's resistance to changes in its own current, not its ability to induce emf in another coil.

Correct Answer: False

Solution:

Faraday showed that relative motion is not an absolute requirement; a changing magnetic field can also induce current without relative motion.

Correct Answer: False

Solution:

The induced current is larger when the magnet is moved faster towards or away from the coil.

Correct Answer: False

Solution:

Faraday's experiments showed that relative motion is not an absolute requirement for inducing current; a change in magnetic flux can also induce current.

Correct Answer: True

Solution:

Faraday's experiments showed that relative motion between a magnet and a coil induces electric current, as observed with a galvanometer.

Correct Answer: False

Solution:

A galvanometer shows deflection only when there is relative motion between the magnet and the coil, not when the magnet is stationary.

Correct Answer: False

Solution:

A steady current in a coil can induce a current in a nearby coil if there is a change in the current, as shown by Faraday's experiments.

Correct Answer: False

Solution:

Faraday's experiments showed that it is the relative motion between a magnet and a coil that induces an electric current, not a stationary magnet.

Correct Answer: False

Solution:

Faraday's experiments showed that relative motion is not an absolute requirement for inducing current; a change in the magnetic field can also induce current.

Correct Answer: True

Solution:

Electromagnetic induction involves generating electric current through changing magnetic fields, as demonstrated by Faraday and Henry.

Correct Answer: True

Solution:

When a galvanometer connected to a coil shows deflection, it indicates that an electric current is present in the coil.

Correct Answer: False

Solution:

Lenz's law states that the induced current will oppose the change in magnetic flux that produces it.

Correct Answer: True

Solution:

Initially, electricity and magnetism were thought to be unrelated, but experiments by scientists like Oersted and Ampere established their interrelation.

Correct Answer: True

Solution:

The self-inductance of a coil is indeed a measure of its inertia against the change of current through it.

Correct Answer: True

Solution:

An AC generator uses electromagnetic induction to convert mechanical energy into electrical energy by rotating a coil in a magnetic field.

Correct Answer: False

Solution:

A changing current in a coil can induce an emf in a nearby coil, but a steady current will not induce any emf unless there is a change.

Correct Answer: True

Solution:

Lenz's law states that the induced emf will generate a current opposing the change in magnetic flux, which is indicated by the negative sign in Faraday's law.

Correct Answer: True

Solution:

Michael Faraday and Joseph Henry showed that electric currents were induced in closed coils when subjected to changing magnetic fields.

Correct Answer: False

Solution:

The self-inductance of a solenoid depends on the relative permeability of the material inside it.

Correct Answer: False

Solution:

A stationary magnet cannot induce an electric current in a stationary coil. It is the relative motion between the magnet and the coil that induces current.

Correct Answer: False

Solution:

The self-inductance of a solenoid depends on the relative permeability of the core material.

Correct Answer: True

Solution:

Initially, electricity and magnetism were considered separate and unrelated phenomena until experiments by Oersted and Ampere established their interrelation.

Correct Answer: False

Solution:

The self-inductance of a coil depends on the number of turns, as it is related to the flux linkage per unit current, which increases with more turns.

Correct Answer: True

Solution:

This is Lenz's law, which states that the induced current will flow in a direction that opposes the change in magnetic flux.

Correct Answer: False

Solution:

Oersted and Ampere's experiments established that electricity and magnetism are inter-related, showing that moving electric charges produce magnetic fields.

Correct Answer: True

Solution:

Faraday's experiments showed that electric currents were induced in closed coils when subjected to changing magnetic fields, which is the basis of electromagnetic induction.

Correct Answer: True

Solution:

According to Faraday's laws of induction, the emf induced in a coil is directly related to the rate of change of magnetic flux through it.

Correct Answer: True

Solution:

Magnetic flux is defined similarly to electric flux, as mentioned in the context of Faraday's experiments.

Correct Answer: False

Solution:

Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that produces it, not enhances it.

Correct Answer: True

Solution:

This statement is a restatement of Lenz's law, which states that the induced current will oppose the change in magnetic flux.

Correct Answer: True

Solution:

When the current in one coil changes, it can induce an emf in a nearby coil, a phenomenon known as mutual inductance.

Correct Answer: True

Solution:

Electromagnetic induction is not merely of theoretical interest but also of practical utility, leading to the development of generators and transformers.

Correct Answer: False

Solution:

According to Lenz's law, the direction of the induced current is such that it opposes the change in magnetic flux that produces it.

Correct Answer: True

Solution:

Self-inductance is a measure of the inertia of the coil against the change of current through it.

Correct Answer: False

Solution:

A steady magnetic field does not induce an electric current in a stationary coil; a changing magnetic field is required.

Correct Answer: False

Solution:

According to Lenz's law, the direction of the induced current is such that it opposes the change in magnetic flux that produces it.

Correct Answer: True

Solution:

When the direction of motion of the magnet is reversed, the direction of the induced current also reverses, as observed in Faraday's experiments.

Correct Answer: True

Solution:

According to Faraday's laws of induction, the emf induced in a coil is directly related to the rate of change of magnetic flux through it.

Correct Answer: False

Solution:

Faraday's experiments demonstrated that relative motion is not an absolute requirement for electromagnetic induction, as shown in experiments involving stationary coils.

Correct Answer: False

Solution:

A steady current in a coil cannot induce an electric current in a nearby stationary coil; the current must be changing to induce an emf.

Correct Answer: False

Solution:

Faraday's experiments demonstrated that a changing magnetic field, not a steady current, induces an emf in a nearby coil.

Correct Answer: False

Solution:

A steady current in a coil does not induce an emf in a nearby coil; an emf is induced only when there is a change in current.

Correct Answer: False

Solution:

Faraday demonstrated that relative motion is not an absolute requirement for electromagnetic induction. A change in magnetic flux can also induce a current.

Correct Answer: True

Solution:

The self-inductance of a solenoid is given by the formula

L = \mu_r \mu_0 n^2 A l

, where

\mu_r

is the relative permeability of the core material.

Correct Answer: True

Solution:

The self-inductance of a solenoid is given by the formula

L = \mu_r \mu_0 n^2 A l

, where

n

is the number of turns per unit length.

Correct Answer: True

Solution:

Faraday's law states that the induced emf in a coil is directly related to the rate of change of magnetic flux through it, which is a fundamental principle of electromagnetic induction.

Correct Answer: True

Solution:

Lenz's law indicates that the induced emf and current will be in a direction that opposes the change in magnetic flux that caused them.

Correct Answer: False

Solution:

Faraday's experiments showed that relative motion between a magnet and a coil is necessary to induce an electric current.

Correct Answer: True

Solution:

Faraday's experiments showed that electric currents were induced in closed coils when subjected to changing magnetic fields, establishing the principle of electromagnetic induction.

Correct Answer: False

Solution:

The discovery of electromagnetic induction is crucial to modern technology, enabling the development of generators and transformers that power electrical systems.

Correct Answer: True

Solution:

When a metal rod is placed normal to a uniform magnetic field and moved with a velocity perpendicular to the field, an induced emf is generated across its ends.

Correct Answer: True

Solution:

Magnetic flux is defined similarly to electric flux, as both involve the concept of field lines passing through a surface.

Correct Answer: True

Solution:

Oersted and Ampere showed that electricity and magnetism are inter-related, specifically that moving electric charges produce magnetic fields.

Electromagnetic Induction

AI Learning Assistant

Summary

Chapter Six: Electromagnetic Induction

Summary

Key Formulas and Definitions

Learning Objectives

Learning Objectives

Detailed Notes

Chapter Six: Electromagnetic Induction

6.1 Introduction

6.2 Key Concepts

Magnetic Flux

Faraday's Laws of Induction

Lenz's Law

Induced EMF Formulas

6.3 Examples

6.4 Important Formulas and Definitions

6.5 Points to Ponder

Exam Tips & Common Mistakes

Common Mistakes and Exam Tips

Common Pitfalls

Exam Tips

Practice & Assessment

Multiple Choice Questions

Q1.What happens to the galvanometer reading when a coil connected to it is moved towards a stationary coil connected to a battery?

Correct Answer: A

Q2.In an AC generator, a coil with NNN turns and area AAA is rotated at VVV revolutions per second in a uniform magnetic field BBB. What is the expression for the motional emf produced?

Correct Answer: A

Q3.Consider a solenoid with a core of relative permeability μr\mu_rμr​ and a coil of NNN turns per unit length. If the solenoid has a length lll and cross-sectional area AAA, what is the expression for the self-inductance LLL of the solenoid?

Correct Answer: A

Q4.Two coils, C1C_1C1​ and C2C_2C2​, are aligned along a common axis. Coil C2C_2C2​ is connected to a battery and a tapping key. What is observed in coil C1C_1C1​ when the key is pressed?

Correct Answer: A

Q5.What is the effect on the galvanometer when a coil connected to it is moved towards a stationary magnet?

Correct Answer: A

Q6.In an AC generator, a coil of 100 turns and area 0.1 m² is rotated at 50 revolutions per second in a uniform magnetic field of 0.2 T. What is the maximum emf produced?

Correct Answer: B

Q7.What is the role of a galvanometer in electromagnetic induction experiments?

Correct Answer: B

Q8.What is the role of the tapping key in the experiment involving two coils and a galvanometer?

Correct Answer: A

Q9.Which of the following statements best describes electromagnetic induction?

Correct Answer: A

Q10.A circular loop of wire is shrinking in size while placed in a constant magnetic field perpendicular to its plane. What happens to the induced emf in the loop?

Correct Answer: A

Q11.According to Faraday's law, what is directly related to the induced electromotive force (emf) in a coil?

Correct Answer: B

Q12.In Faraday's experiment, what is the effect of inserting an iron rod into the coils?

Correct Answer: C

Q13.Which of the following statements best describes the principle of electromagnetic induction?

Correct Answer: A

Q14.In Faraday's experiments, what happens when the north pole of a bar magnet is pushed towards a coil connected to a galvanometer?

Correct Answer: B

Q15.Which of the following scenarios will result in the maximum induced emf in a coil according to Faraday's law of electromagnetic induction?

Correct Answer: B

Q16.Consider a scenario where a rectangular loop of wire is placed in a uniform magnetic field that is perpendicular to the plane of the loop. The magnetic field is increasing at a constant rate. Which of the following statements is true about the induced current in the loop?

Correct Answer: B

Q17.According to Lenz's Law, what is the direction of the induced current when a north pole of a magnet is moved towards a coil?

Correct Answer: B

Q18.A long solenoid with 15 turns per cm has a small loop of area 2.0 cm² placed inside it normal to its axis. If the current carried by the solenoid changes steadily from 2.0 A to 4.0 A in 0.1 s, what is the induced emf in the loop while the current is changing?

Correct Answer: A

Q19.What is the effect on the induced current when an iron rod is inserted into the coils along their axis?

Correct Answer: A

Q20.In an experiment, a coil connected to a galvanometer shows a deflection when a magnet is moved towards it. What does this indicate?

Correct Answer: B

Q21.A long solenoid with a core of magnetic material has a self-inductance given by L=μrμ0n2AlL = \mu_r \mu_0 n^2 AlL=μr​μ0​n2Al. Which of the following changes will increase the self-inductance?

Correct Answer: A

Q22.What happens when the North-pole of a bar magnet is pushed towards a coil connected to a galvanometer?

Correct Answer: A

Q23.According to Lenz's law, what is the direction of the induced current in a coil when the magnetic flux through it is increasing?

Correct Answer: B

Q24.Which of the following experiments demonstrated that electric currents can be induced in closed coils when subjected to changing magnetic fields?

Correct Answer: A

Q25.In an experiment, a coil is connected to a galvanometer and another coil is connected to a battery. What is observed when the tapping key is pressed?

Correct Answer: B

Q26.Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average emf of 200 V is induced, what is the self-inductance of the circuit?

Correct Answer: A

Q27.In the context of electromagnetic induction, what does the term 'magnetic flux' refer to?

Correct Answer: A

Q28.Which scientist is credited with discovering that electric currents can be induced by changing magnetic fields?