For a coil having\(L=2~\mathrm{mh},\) the current flow through it is \(I=t^2e^{-t}.\) The time at which emf becomes zero is:
1. 2 s
2. 1 s
3. 4 s
4. 3 s

A square of side \(L\) meters lies in the \(XY\text-\)plane in a region where the magnetic field is given by \(\vec{B}=B_{0}\left ( 2\hat{i} +3\hat{j}+4\hat{k}\right )\text{T}\) where \(B_{0}\) is constant. The magnitude of flux passing through the square will be:
1. \(2 B_{0} L^{2}~\text{Wb}\)
2. \(3 B_{0} L^{2}~\text{Wb}\)
3. \(4 B_{0} L^{2}~\text{Wb}\)
4. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)$$

Two identical conductors P and Q are placed on two frictionless (conducting) rails R and S in a uniform magnetic field directed into the plane. If P is moved in the direction as shown in the figure with a constant speed, then rod Q:

Two coaxial coils are very close to each other and their mutual inductance is 5 mH. If a current 50 sin 500t is passed in one of the coils, then the peak value of induced e.m.f. in the secondary coil will be:

With the decrease of current in the primary coil from 2 A to zero in 0.01 s, the e.m.f. generated in the secondary coil is \(1000~\mathrm{V}\). The mutual inductance of the two coils is:

1. 1.25 H

2. 2.50 H

3. 5.00 H

4. 10.00 H

A long solenoid has self-inductance L. If its length is doubled keeping total number of turns constant, then its new self-inductance will be:

1. $\frac{\mathrm{L}}{2}$

2. 2L

3. L

4. $\frac{\mathrm{L}}{4}$

An inductor is connected to a direct voltage source through a switch. Then:

The magnetic energy stored in a long solenoid of an area of cross-section A in a small region of length L is:

1. $\frac{{\mathrm{B}}^2\mathrm{AL}}{2{{\mathrm{\mu }}_0}^2}$

2. $\frac{\mathrm{AL}}{2{\mathrm{\mu }}_0}$

3. $\frac{1}{2}{\mathrm{\mu }}_0{\mathrm{B}}^2\mathrm{AL}$

4. $\frac{{\mathrm{B}}^2\mathrm{AL}}{2{\mathrm{\mu }}_0}$

Eddy currents are induced when:

1. A metal block is kept in a changing magnetic field.

2. A metal block is kept in a uniform magnetic field.

3. A coil is kept in a uniform magnetic field.

4. Current is passed in a coil.