Electromagnetic Induction — CBSE Class 12 board PYQs

A coil of area of cross-section $0.5{\mathrm{m}}^2$ is placed in a magnetic field acting normally to its plane. The field varies as $B=0.5t^2+2t$, where $B$ is in tesla and $t$ in seconds. The emf induced in the coil at $t=1\mathrm{s}$ is

The number of turns of a solenoid is doubled without changing its length and area of cross-section. The self-inductance of the solenoid will become ____ times.

An iron-cored solenoid has a self-inductance of $2.8\mathrm{H}$. When the core is removed, the self-inductance becomes $2\mathrm{mH}$. What is the relative permeability of the core used?

A long straight current-carrying wire passes normally through the centre of a circular loop. If the current through the wire increases, will there be an induced emf in the loop? Justify.

A conducting loop is held below a current-carrying wire PQ as shown. Predict the direction of the induced current in the loop when the current in the wire is constantly increasing.

The motion of a copper plate is damped when it is allowed to oscillate between the two poles of a magnet. If slots are cut in the plate, how will the damping be affected?

How does the mutual inductance of a pair of coils change when
(i) the distance between the coils is decreased, and
(ii) the number of turns in the coils is decreased?

Predict the directions of the induced currents in metal rings 1 and 2 lying in the same plane, where the current $I$ in the straight wire is increasing steadily.

A plot of magnetic flux $(\varphi )$ versus current $(I)$ is shown in the figure for two inductors A and B. Which of the two has the larger value of self-inductance?

When the current in a coil changes with time, how is the back emf induced in the coil related to it?

A solenoid with an iron core and a bulb are connected to a d.c. source. How does the brightness of the bulb change when the iron core is removed from the solenoid?

In a given circuit, an inductor $L$ and a resistor $R$ have identical resistance. Two similar electric lamps $B_1$ and $B_2$ are connected as shown. When the switch $S$ is closed:
(i) Which one of the lamps lights up earlier?
(ii) Will the lamps be equally bright after some t …

(a) State Lenz's law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it, in accordance with the law of conservation of energy. Justify this.
(b) A metal rod of length $2\mathrm{m}$ is rotated with a frequency of $60rev/s$ a …

State Lenz's law. Explain, by giving examples, that Lenz's law is a consequence of conservation of energy.

(a) Define the term 'self-inductance' and write its S.I. unit.
(b) Obtain the expression for the mutual inductance of two long co-axial solenoids $S_1$ and $S_2$ wound one over the other, each of length $L$ and radii $r_1$ and $r_2$, with $n_1$ and $n_2$ turns per uni …

(i) Define mutual inductance.
(ii) A pair of adjacent coils has a mutual inductance of $1.5\mathrm{H}$. If the current in one coil changes from $0$ to $20\mathrm{A}$ in $0.5\mathrm{s}$, what is the change of flux linkage with the other coil?

(a) A rod of length $\ell$ is moved horizontally with a uniform velocity $v$ in a direction perpendicular to its length through a region in which a uniform magnetic field is acting vertically downward. Derive the expression for the emf induced across the ends of the rod.
(b) How …

A rectangular conductor LMNO is placed in a uniform magnetic field of $0.5\mathrm{T}$, directed perpendicular to the plane of the conductor. When the arm MN of length $20\mathrm{cm}$ is moved towards the left with a velocity of $10\mathrm{m}{\mathrm{s}}^{-1}$, calculate the emf indu …

A wheel with 8 metallic spokes, each $50\mathrm{cm}$ long, is rotated with a speed of $120rev/min$ in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is $0.4\mathrm{G}$ and the angle of dip is …

Define self-inductance of a coil. Show that the magnetic energy required to build up the current $I$ in a coil of self-inductance $L$ is given by $\frac{1}{2}L{I}^2$.

A metallic rod of length $L$ is rotated with angular frequency $\omega$ with one end hinged at the centre and the other end at the circumference of a circular metallic ring of radius $L$, about an axis passing through the centre and perpendicular to the plane of the ring. A const …

Two bar magnets are quickly moved towards a metallic loop connected across a capacitor $C$ as shown in the figure. Predict the polarity of the capacitor.

What are eddy currents? Write any two applications of eddy currents.

A coil Q is connected to a low-voltage bulb B and placed near another coil P (connected to an a.c. source) as shown in the figure. Give reasons to explain the following observations:
(a) the bulb B lights;
(b) the bulb gets dimmer if the coil Q is moved towards the left (away fro …

Derive an expression for the self-inductance of a long air-cored solenoid of length $\ell$ and number of turns $N$.

A jet plane is travelling west at $450{\text{m s}}^{-1}$. If the horizontal component of the earth's magnetic field at that place is $4\times 10^{-4}\text{T}$ and the angle of dip is $30^{\circ }$, find the emf induced between the ends of the wings having a span of …

In the figure, a bar magnet moving towards the right or left induces an emf in the coils (1) and (2). Giving reasons, find the directions of the induced currents through the resistors AB and CD when the magnet is moving (a) towards the right, and (b) towards the left.

A $0.5\mathrm{m}$ long metal rod PQ completes the circuit as shown in the figure. The plane of the circuit is perpendicular to a magnetic field of flux density $0.15\mathrm{T}$. If the resistance of the total circuit is $3\Omega$, calculate the force needed to move the rod …

How is the mutual inductance of a pair of coils affected when
(i) the separation between the coils is increased,
(ii) the number of turns of each coil is increased, and
(iii) a thin iron sheet is placed between the two coils, other factors remaining the same? Explain your answer …

What are eddy currents? How are these produced? In what sense are eddy currents considered undesirable in a transformer, and how are these reduced in such a device?

A circular coil of radius $8\mathrm{cm}$ and $20$ turns rotates about its vertical diameter with an angular speed of $50{\mathrm{s}}^{-1}$ in a uniform horizontal magnetic field of magnitude $3\times 10^{-2}\mathrm{T}$. Find the maximum and average value of the emf induced i …

Define self-inductance and give its S.I. unit. Derive an expression for the self-inductance of a long, air-cored solenoid of length $\ell$, radius $r$, and having $N$ number of turns.

A rectangular loop and a circular loop are moving out of a uniform magnetic field to a field-free region with a constant velocity. The field is normal to the plane of both loops. Draw the expected shape of the graphs showing the variation of the flux with time in both cases. What …

(i) Define the coefficient of self-induction and obtain an expression for the self-inductance of a long solenoid of length $\ell$, area of cross-section $A$, having $N$ turns.
(ii) Calculate the self-inductance of a coil using the data obtained when an AC source of frequency …

(i) With the help of a labelled diagram, describe the principle and working of an AC generator. Hence obtain an expression for the instantaneous value of the emf generated.
(ii) The coil of an AC generator consists of $100$ turns of wire, each of area $0.5{\mathrm{m}}^2$. The r …

Consider the experimental set-up shown in the figure. This jumping-ring experiment is a demonstration of simple laws of physics: a conducting non-magnetic ring is placed over the vertical core of a solenoid, and when current is passed through the solenoid, the ring is thrown off. …

An aeroplane is flying horizontally from west to east with a velocity of $900\text{km/hour}$. Calculate the potential difference developed between the ends of its wings having a span of $20\text{m}$. The horizontal component of the Earth's magnetic field is …

(a) When a bar magnet is pushed towards (or away from) a coil connected to a galvanometer, the pointer in the galvanometer deflects. Identify the phenomenon causing this deflection, write the factors on which the amount and direction of the deflection depend, and state the laws d …

(a) Define mutual inductance and write its S.I. unit.
(b) Derive an expression for the mutual inductance of two long coaxial solenoids of the same length wound one over the other.
(c) In an experiment, two coils $c_1$ and $c_2$ are placed close to each other. Find the express …

(a) State Lenz's law and give one example to illustrate it. The Lenz's law is a consequence of the principle of conservation of energy — justify this statement.
(b) Deduce an expression for the mutual inductance of two long coaxial solenoids having different radii and different n …

Explain briefly, with the help of a labelled diagram, the basic principle of the working of an AC generator. In an AC generator, a coil of $N$ turns and area $A$ is rotated at $\nu$ revolutions per second in a uniform magnetic field $B$. Write the expression for the emf produced. …