A uniform magnetic field is restricted within a region of radius r.

The magnetic field changes with time at a rate $\frac{\mathrm{d}\overrightarrow{\mathrm{B}}}{\mathrm{dt}}$. Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of the magnetic field as shown in the figure below. Then the emf generated is

                        

1.  $-\frac{\mathrm{d}\overrightarrow{\mathrm{B}}}{\mathrm{dt}} {\mathrm{\pi r}}^2$ in loop 1 and $-\frac{\mathrm{d}\overrightarrow{\mathrm{B}}}{\mathrm{dt}} {\mathrm{\pi r}}^2$ in loop 2

2.  $-\frac{\mathrm{d}\overrightarrow{\mathrm{B}}}{\mathrm{dt}} {\mathrm{\pi R}}^2$ in loop 1 and zero in loop 2

3.  $-\frac{\mathrm{d}\overrightarrow{\mathrm{B}}}{\mathrm{dt}} {\mathrm{\pi r}}^2$ in loop 1 and zero in loop 2

4.  zero in loop 1 and zero in loop 2

A long solenoid of diameter 0.1 m has $2 \times {10}^4$ turns per meter. At the center of the solenoid, a coil of 100 turns and a radius 0.01 m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to 0 A from 4 A in 0.05 s. If the resistance of the coil is 10 ${\mathrm{\pi }}^2\mathrm{\Omega }$, the total charge flowing through the coil during this time is

1.  16 $\mathrm{\mu C}$

2.  32 $\mathrm{\mu C}$

3.  16 $\pi \mathrm{\mu C}$

4.  32 $\pi \mathrm{\mu C}$

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.  1.389 H

2.  138.88 h

3.  0.138 H

4.  13.89 H

The ozone layer blocks the radiations of wavelength

1.  less than 3 x ${10}^{-7}$ m.

2.  equal to 3 x ${10}^{-7}$ m.

3.  more than 3 x ${10}^{-7}$ m.

4.  All of the above.

An electron moves on a straight-line path XY as shown below,abcd is a coil adjacent to the path of the electron. What will be the direction of the current, if any induced in the coil?

1.  No current-induced

2.  abcd

3.  adcd

4.  The current will reverse its direction as the electron goes past the coil.

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is

1.  Once per revolution

2.  Twice per revolution

3.  Four times per revolution

4.  Six-time per revolution

In a coil of resistance 10 $\mathrm{\Omega }$, the induced current developed by changing magnetic flux through it is shown in the figure as a function of time. The magnitude of change in flux through the coil in Weber is:

1.  6

2.  4

3.  8

4.  2

Alternating electric field of frequency v, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by

1.  $\mathrm{B}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{2\mathrm{\pi mv}}{\mathrm{e}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{K}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>2{\mathrm{m\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

2.  $\mathrm{B}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{\mathrm{mv}}{\mathrm{e}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{k}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{m}}^2{\mathrm{\pi vR}}^2$

3.  $\mathrm{B}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{\mathrm{mv}}{\mathrm{e}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{K}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>2{\mathrm{m\pi }}^2{\mathrm{v}}^2\mathrm{R}$

4.  $\mathrm{B}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>\frac{2\mathrm{\pi mv}}{\mathrm{e}}<mspace\; width="1em"></mspace>\mathrm{and}<mspace\; width="1em"></mspace>\mathrm{K}<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\mathrm{m}}^2{\mathrm{\pi vR}}^2$

A coil of resistance of 400$\Omega$ is placed in a magnetic field. If the magnetic flux $\varphi \left(Wb\right)$ linked with the coil varies with time t(s) as $\varphi <mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>50t^2<mspace\; width="1em"></mspace>+\hspace{0.17em}4$, the current in the coil at t = 2 s is -

1.  2A

2.  1A

3.  0.5A

4.  0.1A

A conducting circular loop is placed in a uniform magnetic field 0.04 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm ${\mathrm{s}}^{-1}$. The induced emf in the loop when the radius is 2 cm is

1.  4.8$\mathrm{\pi \mu V}$

2.  0.8$\mathrm{\pi \mu V}$

3.  1.6$\mathrm{\pi \mu V}$

4.  3.2$\mathrm{\pi \mu V}$