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. | \(1\) and zero in loop \(2\) | zero in loop
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. | \(1\) and not defined in loop \(2\) | zero in loop
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:
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.
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. |