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. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)$$

A loop, made of straight edges has six corners at A(0, 0, 0), B(L, 0, 0), C(L, L, 0), D(0, L, 0), E(0, L, L) and F(0, 0, L). A magnetic field B=${\mathrm{B}}_0\left(\hat{\mathrm{i}}+\hat{\mathrm{k}}\right)$ T is present in the region. The flux passing through the loop ABCDEFA (in that order) is:

1. B₀L² Wb³ 

2. 2B₀L² Wb

3. \(\sqrt2\)B₀L² Wb

4. 4B₀L² Wb

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 \(0.4~\text{G}\). The induced emf between the axle and rim of the wheel will be:
\((1~\text{G}=10^{-4}~\text{T})\)
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)