Q. No.A uniform magnetic field is restricted within a region of radius \(r\). The magnetic field changes with time at a rate \(\frac{dB}{dt}\). Loop \(1\) of radius \(R>r\) is enclosed within the region \(r\) and loop \(2\) of radius \(R\) is outside the region of the magnetic field as shown in the figure. Then, the emf generated is:
1.
zero in loop \(1\) and zero in loop \(2\)
2.
\(-\frac{dB}{dt}\pi r^2\) in loop \(1\) and zero in loop \(2\)
3.
\(-\frac{dB}{dt}\pi R^2\) in loop \(1\) and zero in loop \(2\)
4.
zero in loop \(1\) and not defined in loop \(2\)
An electron moves on a straight-line path \(XY\) as shown. The \(\mathrm{abcd}\) is a coil adjacent to the path of electrons. What will be the direction of current if any, induced in the coil?
| 1. | \(\mathrm{abcd}\) |
| 2. | \(\mathrm{adcb}\) |
| 3. | The current will reverse its direction as the electron goes past the coil |
| 4. | No current included |
A conducting square frame of side \(a\) and a long straight wire carrying current \(I\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v.\) The emf induced in the frame will be proportional to:
1. \( \frac{1}{x^2} \)
2. \( \frac{1}{(2 x-a)^2} \)
3. \( \frac{1}{(2 x+a)^2} \)
4. \(\frac{1}{(2 x-a)(2 x+a)}\)
A thin semicircular conducting the ring \((PQR)\) of radius \(r\) is falling with its plane vertical in a horizontal magnetic field \(B,\) as shown in the figure. The potential difference developed across the ring when it moves with speed \(v\) is:
| 1. | zero |
| 2. | \(Bv\pi r^{2}/2\) and \(P\) is at a higher potential |
| 3. | \(\pi rvB\) and \(R\) is at a higher potential |
| 4. | \(2BvR\) and \(R\) is at higher potential |
| 1. | number of turns in the coil is reduced. |
| 2. | a capacitance of reactance \(X_C = X_L\) is included in the same circuit. |
| 3. | an iron rod is inserted in the coil. |
| 4. | frequency of the AC source is decreased. |
| 1. | twice per revolution. |
| 2. | four times per revolution. |
| 3. | six times per revolution. |
| 4. | once per revolution. |
A coil of resistance \(400~\Omega\) is placed in a magnetic field. The magnetic flux \(\phi~\text{(Wb)}\) linked with the coil varies with time \(t~\text{(s)}\) as \(\phi=50t^{2}+4.\) The current in the coil at \(t=2~\text{s}\) is:
1. \(0.5~\text{A}\)
2. \(0.1~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)
The current (\(I\)) in the inductance is varying with time (\(t\)) according to the plot shown in the figure.
Which one of the following is the correct variation of voltage with time in the coil?
| 1. |  |
2. |  |
| 3. |  |
4. |  |
The current \(i\) in a coil varies with time as shown in the figure. The variation of induced emf with time would be:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
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