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. $\frac{L{i}^{2}B}{4\mathrm{\pi }}$

Three long, straight parallel wires carrying current, are arranged as shown in figure. The force experienced by a 25 cm length of wire C is

(1) ${10}^{-3}N$

(2) $2.5\times {10}^{-3}N$

(3) Zero

(4) $1.5\times {10}^{-3}N$

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current I along the same direction as shown in the figure. 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. $\frac{{\mu }_o{i}^2}{\sqrt{2}\mathrm{\pi d}}$