Q. No.The magnetic potential energy stored in a certain inductor is \(25\) mJ, when the current in the inductor is \(60\) mA. This inductor is of inductance:
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H
1. \(0.138\) H
2. \(138.88\) H
3. \(1.389\) H
4. \(13.89\) H
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 coil of self-inductance \(L\) is connected in series with a bulb \(\mathrm{B}\) and an AC source. The brightness of the bulb decreases when:
| 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. |
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 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 e.m.f. in the loop when the radius is 2 cm is:
1. \(3.2\pi ~\mu V\)
2. \(4.8\pi ~\mu V\)
3. \(0.8\pi ~\mu V\)
4. \(1.6\pi ~\mu V\)
A rectangular, a square, a circular, and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, . The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops out of the field region, will not remain constant for:
| 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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