Q. No.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. \(\frac{1}{(2 x-a)(2 x+a)}\)
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. |  |
A conducting circular loop is placed in a uniform magnetic field, \(B=0.025~\text{T}\) with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of \(1~\text{mm s}^{-1}\). The induced emf, when the radius is \(2~\text{cm}\), is:
1. \(2\pi ~\mu\text{V}\)
2. \(\pi ~\mu\text{V}\)
3. \(\dfrac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)
A conducting circular loop is placed in a uniform magnetic field of \(0.04\) T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at a rate of \(2\) mm/s. The induced emf in the loop when the radius is \(2\) cm is:
1. \(3.2\pi ~\mu \text{V}\)
2. \(4.8\pi ~\mu\text{V}\)
3. \(0.8\pi ~\mu \text{V}\)
4. \(1.6\pi ~\mu \text{V}\)
| 1. | the rectangular, circular, and elliptical loops. |
| 2. | the circular and the elliptical loops. |
| 3. | only the elliptical loop. |
| 4. | any of the four loops. |
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