In a moving coil galvanometer, the deflection of the coil $\theta$ is related to the electrical current i by the relation

1. $i\propto \tan \theta$                 

2. $i\propto \theta$ 

3. $i\propto {\theta }^2$                    

4. $i\propto \sqrt{\theta }$ 

A moving coil galvanometer has N number of turns in a coil of effective area A, it carries a current I. The magnetic field B is radial. The torque acting on the coil is 
 

1. $N{A}^2{B}^{2}I$                          

2. $NAB{I}^2$

3. $N^{2}ABI$                            

4. $NABI$

If a particle of charge ${10}^{-12}$ coulomb moving along the $\hat{x} -$ direction with a velocity ${10}^5$ m/s experiences a force of ${10}_{}^{-10}$ newton in $\hat{y}$- direction due to magnetic field, then the minimum magnetic field is 

1.  $6.25\times {10}^3$ tesla in $\hat{z}$- direction

2.  ${10}^{-15}$  tesla in $\hat{z}$- direction

3.  $6.25\times {10}^{-3}$ tesla in $\hat{z}$- direction

4.  ${10}^{-3}$ tesla in $\hat{z}$- direction 

A small coil of N turns has an effective area A and carries a current I. It is suspended in a horizontal magnetic field $\stackrel{.}{B}$ such that its plane is perpendicular to $\stackrel{.}{B}$. The work done in rotating it by $180°$ about the vertical axis is 

1. $NAIB$                               2. $2NAIB$ 

3. $2\mathrm{\pi NAIB}$                           4. $4\mathrm{\pi }NAIB$

An electron moves with a constant speed v along a circle of radius r. Its magnetic moment will be (e is the electron's charge)

1. evr                       

2. $\frac{1}{2}$evr 

3. ${\mathrm{\pi r}}^2$ev                    

4. 2$\mathrm{\pi }$rev 

Four wires each of length 2.0 metres are bent into four loops P, Q, R and S and then suspended into uniform magnetic field. Same current is passed in each loop. Which statement is correct?

1. Couple on loop P will be the highest

2. Couple on loop Q will be the highest

3. Couple on loop R will be the highest

4. Couple on loop S will be the highest

A circular current carrying coil has a radius R. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{8}\mathrm{th}$ to its value at the centre of the coil, is

1. $\frac{\mathrm{R}}{\sqrt{3}}$                       

2.  $\mathrm{R}\sqrt{3}$

3. $2\sqrt{3}\mathrm{R}$                     

4. $\frac{2}{\sqrt{3}}\mathrm{R}$

Which among the following options needs to be decreased to increase the sensitivity of a moving coil galvanometer?

A metallic loop is placed in a magnetic field. If a current is passed through it, then

1. The ring will feel a force of attraction

2. The ring will feel a force of repulsion

3. It will move to and fro about its centre of gravity

4. None of these

A straight wire carrying a current i is turned into a circular loop. If the magnitude of the magnetic moment associated with it in M.K.S. unit is M, the length of wire will be

1. $4\mathrm{\pi iM}$                          2. $\sqrt{\frac{4\mathrm{\pi M}}{i}}$

3. $\sqrt{\frac{4\mathrm{\pi i}}{M}}$                        4. $\frac{M\mathrm{\pi }}{4i}$