The magnetic flux linked with a coil (in Wb) is given by the equation \(\phi=5 t^2+3 t+60\). The magnitude of induced emf in the coil at \(t=4\) s  will be:
1. \(33\) V
2. \(43\) V
3. \(108\) V
4. \(10\) V

A wheel with \(20\) metallic spokes, each \(1\) m long, is rotated with a speed of \(120\) rpm in a plane perpendicular to a magnetic field of \(0.4\) G. The induced emf between the axle and rim of the wheel will be:
\((1~\mathrm{G}=10^{-4}~\mathrm{T})\)
1. \(2.51 \times10^{-4}\) V
2. \(2.51 \times10^{-5}\) V
3. \(4.0 \times10^{-5}\) V
4. \(2.51\) V

A cylindrical bar magnet is rotated about its axis. A wire is connected from the axis and is made to touch the cylindrical surface through a contact. Then:

Q. 4. There are two coils A and B as shown in the figure. A current starts flowing in B as shown when A is moved towards B and stops when A stops moving. The current in A is counterclockwise. B is kept stationary when A moves. We can infer that:

1. there is a constant current in the clockwise direction in A

2. there is a varying current in A

3. there is no current in A

4. there is a constant current in the counterclockwise direction in A

Q. 5. Same as problem 4 except coil A is made to rotate about a vertical axis (figure). No current flows in B if A is at rest. The current in coil A, when the current in B (at t-0) is counter-clockwise and the coil A is as shown at this instant, t=0, is:

1. constant current clockwise

2. varying current clockwise

3. varying current counterclockwise

4. constant current counterclockwise

The self-inductance \(L\) of a solenoid of length \(l\) and area of cross-section \(A\), with a fixed number of turns \(N\) increases as:

A metal plate is getting heated. It can be because:

(1). (a, b, d)
(2). (a, c, d)
(3). (b, c, d)
(4). (a, b, c)

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to:

(1). (a, c, d)
(2). (a, b, d)
(3). (b, c, d)
(4). (a, b, c)

Q. 9. The mutual inductance M₁₂ of coil 1 with respect to coil 2

(a) increases when they are brought nearer

(b) depends on the current passing through the coils

(c) increases when one of them is rotated about an axis

(d) is the same as M₂₁ of coil 2 with respect to coil 1

(1) (a, c)

(2) (b, c)

(3) (a, d)

(4) (c, d)

A square loop of side \(10~\text{cm}\) and resistance \(0.5~\Omega\)$$ is placed vertically in the east-west plane. A uniform magnetic field of \(0.10~\text{T}\) is set up across the plane in the north-east direction. The magnetic field is decreased to zero in \(0.70~\text{s}\) at a steady rate. The magnitude of induced current during this time interval is:
1. \(2~\text{mA}\)
2. \(1~\text{mA}\)
3. \(0.5~\text{mA}\)
4. \(3~\text{mA}\)