Q. No.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. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)
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. \(\sqrt{29} B_{0} L^{2}~\text{Wb}\)
The direction of the induced current \(I\) in the figure is:
| 1. | From \(a\) to \(b\) and from \(c\) to \(d\) |
| 2. | From \(a\) to \(b\) and from \(f\) to \(e\) |
| 3. | From \(b\) to \(a\) and from \(d\) to \(c\) |
| 4. | From \(b\) to \(a\) and from \(e\) to \(f\) |
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 \(Q\):
| 1. | will be attracted toward \(P\). |
| 2. | will be repelled away from \(P\). |
| 3. | will remain stationary. |
| 4. | maybe repelled or attracted towards \(P\). |
| 1. | \(5000\) V | 2. | \(500\) V |
| 3. | \(150\) V | 4. | \(125\) V |
With the decrease of current in the primary coil from \(2\) A to zero in \(0.01\) s, the emf generated in the secondary coil is \(1000~\text{V}\). 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. \(\frac{L}{2}\)
2. \(2L\)
3. \(L\)
4. \(\frac{L}{4}\)
An inductor is connected to a direct voltage source through a switch. Then:
| 1. | a very large emf is induced in inductor when the switch is closed. |
| 2. | a large emf is induced when the switch is opened. |
| 3. | a large emf is induced whether the switch is closed or opened. |
| 4. | no emf is induced whether the switch is closed or opened. |
| 1. | \(\dfrac{B^{2} AL}{2\mu_{0}^{2}}\) | 2. | \(\dfrac{AL}{2 \mu_{0}}\) |
| 3. | \(\dfrac{1}{2} \mu_{0} B^{2} AL\) | 4. | \(\dfrac{B^{2} AL}{2 \mu_{0}}\) |
When a conducting wire \(XY\) is moved towards the right, a current flows in the anti-clockwise direction. Direction of magnetic field at point \(O\) is:
| 1. | parallel to the motion of wire. |
| 2. | along with \(XY\). |
| 3. | perpendicular outside the paper. |
| 4. | perpendicular inside the paper. |
A bar magnet is made to fall through a long surface copper tube. The speed \((v)\) of the magnet as a function of time \((t)\) is best represented by:
| 1. | \(a\) | 2. | \(b\) |
| 3. | \(c\) | 4. | \(d\) |
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