A ring of radius R, made of an insulating material carries a charge Q uniformly distributed on it. If the ring rotates about the axis passing through its center and normal to the plane of the ring with constant angular speed $\omega$, then the magnitude of the magnetic moment of the ring is:

1. $Q\omega R^2$                       2. $\frac{1}{2}Q\omega R^2$

3. $Q{\omega }^{2}R$                       4. $\frac{1}{2}Q{\omega }^{2}R$

Three long, straight and parallel wires carrying currents are arranged as shown in the figure. The wire C which carries a current of 5.0 amp is so placed that it experiences no force. The distance of wire C from wire D is then 

1. 9 cm                                         

2. 7 cm 

3. 5 cm                                          

4. 3 cm

If m is the magnetic moment and B is the magnetic field, then the torque is given by

(1) $\overrightarrow{m}.\overrightarrow{B}$                      
(2) $\frac{\left|\overrightarrow{m}\right|}{\left|\overrightarrow{B}\right|}$
(3) $\overrightarrow{m}\times \overrightarrow{B}$                     
(4) $\left|\overrightarrow{m}\right|.\left|\overrightarrow{B}\right|$

What is the net force on the square coil?

(1) $1.67\times {10}^{-6}N$ moving towards wire

(2) $25\times {10}^{-7}N$ moving away from wire

(3) $35\times {10}^{-7}N$ moving towards wire

(4) $35\times {10}^{-7}N$ moving away from wire

A long wire A carries a current of 10 amp. Another long wire B, which is parallel to A and separated by 0.1m from A, carries a current of 5 amp, in the opposite direction to that in A. what is the magnitude and nature of the force experienced per unit length of B $({\mu }_0=4\mathrm{\pi }\times {10}^{-7}weber/amp-\mathrm{m})$

1. repulsive force of ${10}^{-4}N/m$

2. attractive force of ${10}^{-4}N/m$

3. repulsive force of $2\mathrm{\pi }\times {10}^{-5}\mathrm{N}/\mathrm{m}$

4. attractive force of $2\mathrm{\pi }\times {10}^{-5}\mathrm{N}/\mathrm{m}$

The relation between voltage sensitivity (${\sigma }_v$) and current sensitivity (${\sigma }_i$) of a moving coil galvanometer is (Resistance of Galvanometer = G) 

1. $\frac{{\sigma }_i}{G}={\sigma }_v$                           

2. $\frac{{\sigma }_v}{G}={\sigma }_i$

3. $\frac{G}{{\sigma }_v}={\sigma }_i$                           

4. $\frac{G}{{\sigma }_i}={\sigma }_v$

\(A,B, ~\text{and}~C\) are parallel conductors of equal length carrying currents \(I, I,~\text{and}~2I\) respectively. The distance between \(A\) and \(B\) is \(x\). The distance between \(B~\text{and}~C\) is also \(x\). \(F_1\) is the force exerted by \(B\) on \(A\) and \(F_2\) is the force exerted by \(C\) on \(A\) choose the correct answer:

                       
1. \(F_1 = 2F_2\)
2. \(F_2 = 2F_1\)
3. \(F_1 = F_2\)
4. \(F_1 = -F_2\)

Two galvanometers A and B require 3mA and 5mA respectively to produce the same deflection of $i_0$ divisions. Then

(1) A is more sensitive than B

(2) B is more sensitive than A

(3) A and B are equally sensitive

(4) Sensitiveness of B is 5/3 times that of A

There long straight wires A, B and C are carrying current as shown figure. Then the resultant force on B is directed 

Current i is carried in a wire of length L. If the wire is turned into a circular coil, the maximum magnitude of torque in a given magnetic field B will be:

1. $\frac{Li{B}^2}{2}$                     2. $\frac{L{i}^{2}B}{2}$

3. $\frac{L^{2}iB}{4\mathrm{\pi }}$                     4. $\frac{L{i}^{2}B}{4\mathrm{\pi }}$