Electromagnetic Induction — Class 12 Physics PYQs

A circular coil of diameter 15 mm having 300 turns is placed in a magnetic field of 30 mT such that the plane of the coil is perpendicular to the direction of magnetic field. The magnetic field is reduced uniformly to zero in 20 ms and again increased uniformly to 30 mT in 40 ms. If the emfs induced in the two time intervals are $e_1$ and $e_2$ respectively, then the value of $e_1/e_2$ is
(A) $\frac{1}{2}$
(B) 1
(C) 2
(D) 4

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be
(A) 2592
(B) 2866
(C) 2976
(D) 3140

In the figure X is a coil wound over a hollow wooden pipe.
A permanent magnet is pushed at a constant speed v from the right into the pipe and it comes out at the left end of the pipe. During the entry and the exit of the magnet, the current in the wire YZ will be from
(A) Y to Z and then Y to Z
(B) Z to Y and then Y to Z
(C) Y to Z and then Z to Y
(D) Z to Y and then Z to Y

Two long solenoids of radii $r_1$ and $r_2$ ($>r_1$) and number of turns per unit length $n_1$ and $n_2$ respectively are co-axially wrapped one over the other. The ratio of self-inductance of inner solenoid to their mutual inductance is –
(A) $\frac{n_1}{n_2}$
(B) $\frac{n_2}{n_1}$
(C) $\frac{n_1{r}_1^2}{n_2{r}_2^2}$
(D) $\frac{n_2{r}_1^2}{n_1{r}_2^2}$

Consider two long co-axial solenoids $S_1$ and $S_2$, each of length l (>> $r_2$) and of radius $r_1$ and $r_2$ ($r_2>r_1$). The number of turns per unit length are $n_1$ and $n_2$ respectively. Derive an expression for mutual inductance $M_{12}$ of solenoid $S_1$ with respect to solenoid $S_2$. Show that $M_{21}=M_{12}$.

Show that the energy required to build up the current I in a coil of inductance L is $\frac{1}{2}L{I}^2$.
(b) Considering the case of magnetic field produced by air-filled current carrying solenoid, show that the magnetic energy density of a magnetic field B is $\frac{B^2}{2{\mu }_0}$.

State Lenz's law.
(b) In the given figure :
(i) Identify the machine.
(ii) Name the parts P and Q and R of the machine.
(iii) Give the polarities of magnetic poles.
(iv) Write the two ways of increasing the output voltage.

The emf induced in a coil rotating in a magnetic field does not depend upon the following :
(A) Area of the coil
(B) Resistance of the coil
(C) Number of turns in the coil
(D) Angular speed of rotation of the coil

A circular coil of radius 10 cm is placed in a magnetic field $\vec{B}=(1.0\hat{i}+0.5\hat{j})$ mT such that the outward unit vector normal to the surface of the coil is $(0.6\hat{i}+0.8\hat{j})$. The magnetic flux linked with the coil is :
(A) 0.314 $\mu$Wb
(B) 3.14 $\mu$Wb
(C) 31.4 $\mu$Wb
(D) 1.256 $\mu$Wb

A conducting circular loop is placed in a uniform magnetic field B = 50 mT with its plane perpendicular to the magnetic field. The radius of the loop is made to shrink at a constant rate of 1 mm s${}^{-1}$. At the instant the radius of the loop is 4 cm, the induced emf in the loop is :
(A) $\pi \mu$V
(B) 2$\pi \mu$V
(C) 4$\pi \mu$V
(D) 8$\pi \mu$V