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. |
The primary and secondary coils of a transformer have \(50\) and \(1500\) turns respectively. If the magnetic flux \(\phi\) linked with the primary coil is given by \(\phi=\phi_0+4t,\) where \(\phi\) is in Weber, \(t\) is time in seconds, and \(\phi_0\) is a constant, the output voltage across the secondary coil is:
1. \(90~\mathrm{V}\)
2. \(120~\mathrm{V}\)
3. \(220~\mathrm{V}\)
4. \(30~\mathrm{V}\)
Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is:
1. 10 mH
2. 6 mH
3. 4 mH
4. 16 mH
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. \(\frac{\pi}{2}~\mu\text{V}\)
4. \(2 ~\mu \text{V}\)
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. |
The current (\(I\)) in the inductance is varying with time (\(t\)) according to the plot shown in the figure.
1. | 2. | ||
3. | 4. |
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. \(1~\text{A}\)