Chapter 6: Electromagnetic Induction Short Questions | physics Class 12 CBSE

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Chapter 6: Electromagnetic Induction Short Questions | physics Class 12 CBSE | ByteNotes.in

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Question 1

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Define magnetic flux and state its SI unit.

Magnetic flux through a surface is defined as ΦB = B·A = BA cosθ, where θ is the angle between the magnetic field B and the area vector A.
It represents the total magnetic field lines passing through a given surface area.
The SI unit of magnetic flux is the weber (Wb), which is equivalent to tesla metre squared (T m²). Magnetic flux is a scalar quantity.

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Question 2

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State Faraday's law of electromagnetic induction and write its mathematical expression.

Faraday's law states that the magnitude of the induced emf in a circuit is equal to the time rate of change of magnetic flux through the circuit.
Mathematically, ε = −dΦB/dt for a single turn, and ε = −N(dΦB/dt) for a coil of N turns.
The negative sign indicates the direction of the induced emf as given by Lenz's law — it opposes the change in flux that produced it.

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Question 3

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State Lenz's law and explain how it is consistent with conservation of energy.

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 produced it.
If the induced current aided the change in flux, the magnet would accelerate indefinitely without energy input, constituting a perpetual-motion machine — violating conservation of energy.
Instead, work must be done against the opposing force to move the magnet; this mechanical work is converted into electrical energy dissipated as Joule heat, satisfying energy conservation.

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Question 4

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What is motional emf? Write its expression.

Motional emf is the emf induced across the ends of a conductor when it moves through a magnetic field, by changing the magnetic flux enclosed by the circuit.
When a conductor of length l moves with velocity v perpendicular to a uniform magnetic field B, the motional emf is ε = Blv.
It is produced because the Lorentz force qvB on free charge carriers in the moving conductor displaces them, creating a potential difference across its ends.

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Question 5

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Define self-inductance of a coil and state its SI unit.

Self-inductance (L) is the property of a coil by which it opposes any change in the current flowing through it; it is defined as L = NΦB/I.
It is also called the coefficient of self-induction. The self-induced emf is given by ε = −L(dI/dt), which opposes any change (increase or decrease) in current.
The SI unit of self-inductance is henry (H), named after Joseph Henry. Inductance depends only on the geometry of the coil and the permeability of the medium.

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Question 6

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Define mutual inductance and write the expression for induced emf in one coil due to changing current in another.

Mutual inductance (M) is the property of a pair of coils such that a changing current in one coil induces an emf in the neighbouring coil.
It is defined as M = N1Φ1/I2, the ratio of flux linkage in coil 1 to the current in coil 2.
The induced emf in coil 1 is ε1 = −M(dI2/dt); the magnitude depends on the rate of change of current and the mutual inductance M of the pair.

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Question 7

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In Faraday's Experiment 6.1, why does the galvanometer show no deflection when the bar magnet is held stationary near the coil?

The galvanometer shows deflection only when an emf is induced in the coil, which requires a change in the magnetic flux through the coil.
When the bar magnet is held stationary, the magnetic field and the magnetic flux through the coil do not change with time.
Since there is no rate of change of flux (dΦB/dt = 0), Faraday's law gives ε = 0, so no current flows and the galvanometer shows no deflection.

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Question 8

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Why does the galvanometer in Experiment 6.3 show a momentary deflection only when the tapping key is pressed or released, and not while it is held pressed?

When the tapping key K is pressed, the current in coil C2 rises from zero to maximum rapidly, so the magnetic flux through coil C1 increases — inducing a momentary emf.
When the key is held pressed, the current in C2 is constant and steady, so the magnetic flux through C1 does not change; hence dΦB/dt = 0 and no emf is induced.
When the key is released, the current in C2 falls from maximum to zero rapidly, causing a decrease in flux through C1, which again induces a momentary emf in the opposite direction.

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Question 9

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Show that the flux through a coil can be varied by changing B, A, or the angle θ between them.

From the expression ΦB = BA cosθ, the flux depends on three quantities: the magnetic field strength B, the area A of the coil, and the angle θ between B and the area vector A.
Changing B — for example, by moving a magnet toward or away from the coil — changes the flux; this is the method used in Experiments 6.1 and 6.2.
Changing A by shrinking or stretching the coil, or changing θ by rotating the coil in a magnetic field, also alters the flux and induces an emf — all consistent with Faraday's law.

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Question 10

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What is the significance of the equality M12 = M21?

M12 is the mutual inductance of coil 1 with respect to coil 2, and M21 is the mutual inductance of coil 2 with respect to coil 1; the equality M12 = M21 = M holds in general.
This equality is very useful in situations where calculating one of M12 or M21 directly is extremely difficult — for example, when the magnetic field due to the inner solenoid varies across the cross-section of the outer solenoid.
Because of this equality, one can calculate the easier of the two mutual inductances and use it as the value of M for the pair, simplifying calculations considerably.

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Question 11

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Derive the expression for the self-inductance of a long solenoid of n turns per unit length, area A, and length l.

The magnetic field inside a long solenoid carrying current I is B = μ0nI, directed along the axis.
The total flux linkage with the solenoid is NΦB = (nl)(μ0nI)(A) = μ0n²AlI, where nl is the total number of turns.
By definition, L = NΦB/I = μ0n²Al. If the core has relative permeability μr, then L = μrμ0n²Al.

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Question 12

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Why is self-inductance called the electrical inertia or analogue of mass in mechanics?

Self-inductance opposes any change (increase or decrease) in the current through a coil, just as mass (inertia) opposes any change in the velocity of a body in mechanics.
The energy stored in an inductor W = (1/2)LI² is analogous to the kinetic energy (1/2)mv² of a moving body, with L playing the role of mass m and current I playing the role of velocity v.
Work must be done against the back emf to establish a current in an inductor, just as work must be done against inertia to accelerate a mass — reinforcing the analogy.

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Question 13

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Write the expression for energy stored in an inductor and the energy density of a magnetic field.

The energy required to build up a current I in an inductor of self-inductance L is W = (1/2)LI²; this energy is stored as magnetic potential energy in the magnetic field of the inductor.
For a solenoid of volume V = Al, the magnetic energy per unit volume (energy density) is uB = B²/2μ0.
This expression is analogous to the electrostatic energy density uE = (1/2)ε0E² and is valid for any region of space containing a magnetic field.

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Chapter 6: Electromagnetic Induction | Short Questions

Define magnetic flux and state its SI unit.

State Faraday's law of electromagnetic induction and write its mathematical expression.

State Lenz's law and explain how it is consistent with conservation of energy.

What is motional emf? Write its expression.

Define self-inductance of a coil and state its SI unit.

Define mutual inductance and write the expression for induced emf in one coil due to changing current in another.

In Faraday's Experiment 6.1, why does the galvanometer show no deflection when the bar magnet is held stationary near the coil?

Why does the galvanometer in Experiment 6.3 show a momentary deflection only when the tapping key is pressed or released, and not while it is held pressed?

Show that the flux through a coil can be varied by changing B, A, or the angle θ between them.

What is the significance of the equality M12 = M21?

Derive the expression for the self-inductance of a long solenoid of n turns per unit length, area A, and length l.

Why is self-inductance called the electrical inertia or analogue of mass in mechanics?

Write the expression for energy stored in an inductor and the energy density of a magnetic field.

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