An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57\times {10}^{-2}$ T. If the value of e/m is $1.76\times {10}^{11}$ C/kg, the frequency of revolution of the electron is

1. 1 GHz             

2. 100 MHz

3. 62.8 MHz         

4. 6.28 MHz

A long solenoid has 1000 turns. When a current of 4.0 A flows through it, the magnetic flux linked with each turn of the solenoid is $4\times {10}^{-3}$ Wb. The self-inductance of the solenoid is-

1. 3H

2. 2H

3. 1H

4. 4H

A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be:

1. $\frac{{\mu }_{0}Ii}{2\mathrm{\pi }}$             
2. $\frac{2{\mu }_{0}IiL}{3\mathrm{\pi }}$

3. $\frac{{\mu }_{0}IiL}{2\mathrm{\pi }}$           
4. $\frac{2{\mu }_{0}Ii}{3\mathrm{\pi }}$

A wire carrying current l has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while the semicircular portion of radius R is lying in the Y-Z plane. Magnetic field at point O is :


1. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

2. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

3. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

4. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude:

$1. \frac{{\mu }_{0}ne}{2\pi r}$
$2. Zero$
$3. \frac{n^{2}e}{r}$
$4. \frac{{\mu }_{0}ne}{2r}$

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. If the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be

(1)4 MeV

(2) 0.5 MeV

(3) 1.5 MeV

(4) 1 MeV

A rectangular coil of length 0.12 m and width 0.1 m having 50 turns of wire is suspended vertically in a uniform magnetic field of strength 0.2 Wb/m². The coil carries a current of 2 A. If the plane of the coil is inclined at an angle of 30° with the direction of the field, the torque required to keep the coil in stable equilibrium will be:

1. 0.15 Nm

2. 0.20 Nm

3. 0.24 Nm

4. 0.12 Nm

In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be

(1) $\frac{1}{499}G$

(2) $\frac{499}{500}G$

(3) $\frac{1}{500}G$

(4) $\frac{500}{499}G$

Two identical long conducting wires AOB and COD are placed at right angle to each other, with one above other such that O is their common point for the two. The wires carry  I₁ and I₂ currents, respectively. Point P is lying at distance d from 0 along a direction perpendicular to the plane containing the wires. The magnetic field at the point P will be

(1) μ_o/2πd(I₁/I₂)

(2)μ_o/2πd (I₁+I₂)

(3)μ_o/2πd(I₁²-I₂²)

(4)μ_o/2πd(I₁²+I₂²)^1/2