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 

(a) $NAIB$                               (b) $2NAIB$ 

(c) $2\mathrm{\pi NAIB}$                          (d) $4\mathrm{\pi }NAIB$

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. $\frac{M\mathrm{\pi }}{4i}$

A 100 turns coil shown in figure carries a current of 2 amp in a magnetic field $B=0.2Wb/m^2$. The torque acting on the coil is

(a) 0.32 Nm tending to rotate the side AD out of the page

(b) 0.32 Nm tending to rotate the side AD into the page

(c) 0.0032 Nm tending to rotate the side AD out of the page

(d) 0.0032 Nm tending to rotate the side AD into the page