The back emf induced in a coil, when current changes from 1 ampere to zero in one milli-second, is 4 volts. The self-inductance of the coil is:

1. $1 H$                  

2. $4 H$

3. ${10}^{–3} H$              

4. $4$ $\times$ ${10}^{–3} H$

A series combination of inductance (L) and resistance (R) is connected to a battery of emf E. The final value of current depends on:

1. L and R                           

2. E and R 

3. E and L                           

4. E, L, and R

A uniform magnetic field of induction $\mathrm{B}$ is confined to a cylindrical region of radius $\mathrm{R}$. The magnetic field is increasing at a constant rate of $\frac{\mathrm{dB}}{\mathrm{dt}}$ (tesla/second). An electron of charge $\mathrm{q}$, placed at the point $\mathrm{P}$ on the periphery of the field experiences an acceleration of:

A coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:

A conducting circular loop is placed in a uniform magnetic field of 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm is:

1. \(3.2\pi ~\mu V\)

2. \(4.8\pi ~\mu V\)

3. \(0.8\pi ~\mu V\)

4. \(1.6\pi ~\mu V\)

A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, $\overrightarrow{\mathrm{v}}=\mathrm{v}\hat{\mathrm{i}}$. The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for:

Choose the correct option for the above statements:

A coil is wound of a frame of rectangular cross-section. If the linear dimensions of the frame are doubled and the number of turns per unit length of the coil remains the same, then the self inductance increases by a factor of:

A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction $\frac{1}{\pi }$ $\left(\frac{Wb}{m^2}\right)$ in such a way that its axis makes an angle of ${60}^{°}$ with $\overrightarrow{B}$. The magnetic flux linked to the disc will be:
1. 0.02 Wb
2. 0.06 Wb
3. 0.08 Wb
4. 0.01 Wb

An electron moves on a straight-line path XY as shown. The abcd is a coil adjacent to the path of the electron. What will be the direction of the current, if any induced in the coil?