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, and C are parallel conductors of equal length carrying currents I, I, and 2I respectively. Distance between A and B is x. Distance between B 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 

(1) Towards A

(2) Towards C

(3) Perpendicular to the plane of paper and outward

(4) Perpendicular to the plane of paper and inward

Two long conductors, separated by a distance d carry current $I_1$ and $I_2$ in the same direction. They exert a force F on each other. Now the current in one of them is increased to two times and its direction is reversed. The distance is also increased to $3d$. The new value of the force between them is-

1. $-2F$                           

2.  $2F/3$

3. $-2F/3$                           

4. $-F/3$

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

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