In a uniform magnetic field, a ring is rotating about its axis which is parallel to the magnetic field and the magnetic field is perpendicular to the plane of the ring. The induced electric field in the ring:

1.	Is zero.
2.	Depends on the radius of the ring.
3.	Depends on the nature of the material of the ring.
4.	Depends on the product of the magnetic field and speed.

Calculate the self-inductance of a solenoid having 1000 turns and length 1 m. The area of cross-section is 7 cm² and \(\mu_r=1000\)

1. 888 H

2. 0.88 H

3. 0.088 H

4. 88.8 H

A rod having length l and resistance R₀ is moving with speed v as shown in the figure. The current through the rod is:
               
1. $\frac{Blv}{{\displaystyle \frac{R_1{R}_2}{R_1+R_2}}+R_0}$

2. $\frac{\mathrm{Blv}}{{\left({\displaystyle \frac{1}{{\mathrm{R}}_1}}+{\displaystyle \frac{1}{{\mathrm{R}}_2}}+{\displaystyle \frac{1}{{\mathrm{R}}_{\mathrm{o}}}}\right)}^2}$

3. $\frac{Blv}{R_1+R_2+R_0}$

4. $\frac{Blv}{{\displaystyle \frac{1}{R_1}}+{\displaystyle \frac{1}{R_2}}+{\displaystyle \frac{1}{R_0}}}$

A solenoid of inductance L and resistance R is connected to a battery of e.m.f. E. Maximum value of magnetic energy stored in the inductor is:

$1.$ $\frac{E^2}{2R}$
$2.$ $\frac{E^{2}L}{2R^2}$
$3.$ $\frac{E^{2}L}{R}$ $$
$4.$ $\frac{E^{2}L}{2R}$

The coefficient of mutual inductance between two coils depends upon:

A small square loop of wire of side 'l' is placed inside a large square loop of side 'L' (L$\gg$l). If the loops are coplanar and their centres coincide, the mutual inductance of the system is directly proportional to:

1. L/l

2. l/L

3. L²/l

4. l²/L

Two coils have a mutual inductance of 5 mH. The current changes in the first coil according to the equation \(I=I_{0}cos\omega t,\) where \(I_{0}=10~A\) and $\omega$ = 100$\pi$ rad/s. The maximum value of e.m.f. induced in the second coil is:

1. 5$\pi$ Volt

2. 2$\pi$ Volt

3. 4$\pi$ Volt

4. $\pi$ Volt

The current through a choke coil increases from zero to 6 A in 0.3 seconds and an induced emf of 30 V is produced. The inductance of the coil is:

A short magnet is allowed to fall along the axis of a horizontal metallic ring. Starting from rest, the distance fallen by the magnet in one second may be:

1. 4 m

2. 5 m

3. 6 m

4. 7 m

The magnetic flux linked with a coil varies with time as \(\phi = 2t^2-6t+5,\) where \(\phi \) is in Weber and \(t\) is in seconds. The induced current is zero at:
1. \(t=0\)
2. \(t= 1.5~\text{s}\)
3. \(t=3~\text{s}\)
4. \(t=5~\text{s}\)