A metallic rod of mass per unit length of 0.5 kgm^-1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction of 0.25 T is acting on it in the vertical direction. What is the current flowing through the rod to keep it stationary?

1. 7.14 A

2. 5.98 A

3. 14.76 A

4. 11.32 A

The current sensitivity of a moving coil galvanometer is 5 div/mA and its voltage sensitivity (angular deflection per unit voltage applied) is 20 div/V. The resistance of the galvanometer is: 
1. 40 $\Omega$
2. 25 $\Omega$
3. 250 $\Omega$
4. 500 $\Omega$

A 250 turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 $\mathrm{\mu A}$ and subjected to the magnetic field of strength 0.85 T. Work done for rotating the coil by 180° against the torque is:
1. $4.55 \mu J$
2. $2.3 \mu J$
3. $1.15 \mu J$
4. $9.8 \mu J$

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in fig. The magnitude of force per unit length on the middle wire 'B' is given by:
   

1. $\frac{{\mu }_o{i}^2}{2\mathrm{\pi d}}$

2. $\frac{2{\mu }_0{i}^2}{\mathrm{\pi d}}$

3. $\frac{\sqrt{2}{\mu }_o{i}^2}{\pi d}$

4. $\frac{{\mu }_o{i}^2}{\sqrt{2}\mathrm{\pi d}}$

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the center of loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be

1.  nB               
2.  $n^{2}B$
3.  2nB             
4. $2n^{2}B$

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 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 long straight wire of radius 'a' carries a steady current I. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields B and B' at radial distances a/2 and 2a respectively, from the axis of the wire, is:

1. 1/2

2. 1

3. 4

4. 1/4

A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be:
1.  nB
2.  n²B
3.  2nB
4.  2n²B

An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 x 10^-2 T. If the value of e/m is 1.76 x 10¹¹ C/kg, what will be the frequency of revolution of the electron?

1.  1 GHz

2.  100 MHz

3.  62.8 MHz

4.  6.28 MHz