A uniform magnetic field of induction is confined to a cylindrical region of radius . The magnetic field is increasing at a constant rate of (tesla/second). An electron of charge , placed at the point on the periphery of the field experiences an acceleration of:
1. | \(\frac{\mathrm{B}}{(\sqrt{2}+1) \mathrm{r}}\) towards left. |
2. | \(\frac{1}{2} \frac{\mathrm{eR}}{\mathrm{m}} \frac{\mathrm{dB}}{\mathrm{dt}}\) towards right. |
3. | \(\frac{\mathrm{eR}}{2 \mathrm{~m}} \frac{\mathrm{dB}}{\mathrm{dt}}\) towards left. |
4. | zero. |
In the figure shown a square loop of side and resistance is placed near an infinitely long wire carrying a constant current . The sides and are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by about an axis parallel to the long wire and passing through the midpoints of the side and . The total amount of charge which passes through any point of the loop during rotation is –
1.
2.
3.
4. cannot be found because the time of rotation not given.
A short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electrical power dissipated would be –
1. halved
2. the same
3. doubled
4. quadrupled
A coil having number of turns N and cross-sectional area A is rotated in a uniform magnetic field B with an angular velocity . The maximum value of the emf induced in it is –
1.
2.
3.
4.
A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement (s) from the following :
1. The entire rod is at the same electric potential
2. There is an electric field in the rod
3. The electric potential is highest at the center of the rod and decreases towards its ends
4. The electric potential is lowest at the center of the rod and increases towards its ends.
The mutual inductance of a pair of coils is 2H. If the current of the coil changes from 10A to zero in 0.1s, the emf induced in the other coil is –
1. 2 V
2. 20 V
3. 0.2 V
4. 200 V
A current-carrying wire is placed below a coil in its plane, with current flowing as shown.
If the current increases –
1. no current will be induced in the coil
2. an anticlockwise current will be induced in the coil
3. a clockwise current will be induced in the coil
4. the current induced in the coil will be first anticlockwise and then clockwise
The back emf induced in a coil, when current changes from 1 ampere to zero in one milli-second, is 4 volts. The self-inductance of the coil is:
1.
2.
3.
4.
Average energy stored in a pure inductance L when a current i flows through it, is
1.
2.
3.
4.
A small magnet is along the axis of a coil and its distance from the coil is 80 cm. In this position the flux linked with the coil are weber turns. If the coil is displaced 40 cm towards the magnet in 0.08 second, then the induced emf produced in the coil will be -
1. 0.5 mV
2. 1 mV
3. 7 mV
4. 3.5 mV