In the given figure net magnetic field at O will be  i

   

(a) $\frac{{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{4-{\mathrm{\pi }}^2}$                                 (b) $\frac{{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{4+{\mathrm{\pi }}^2}$

(c) $\frac{2{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{4+{\mathrm{\pi }}^2}$                                  (d) $\frac{2{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{\left(4-{\mathrm{\pi }}^2\right)}$

In the following figure a wire bent in the form of a regular polygon of n sides is inscribed in a circle of radius a. Net magnetic field at centre will be \(\left(\theta = \frac{\pi}{n}\right)\)

1. \(\frac{\left(\mu\right)_{o} i}{2 πa} tan \frac{\pi}{n}\)                                               
2. \(\frac{\left(\mu\right)_{0} n i}{2 πa} tan \frac{\pi}{n}\)

3.\(\frac{2}{\pi} \frac{n i}{a} \left(\mu\right)_{0} tan \frac{\pi}{n}\)                                           
4. \(\frac{n i}{2 a} \left(\mu\right)_{0} tan \frac{\pi}{n}\)

 The unit vectors \(\hat{i} ,   \hat{j}   ~\text{and} ~ \hat{k}\) are as shown below. What will be the magnetic field at \(O\) in the following figure?

1. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a} 2 - \frac{\pi}{2} \hat{j}\)             
2. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a}2 + \frac{\pi}{2} \hat{j}\)
3. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a}2 + \frac{\pi}{2} \hat{i}\)             
4. \(\frac{\mu_{0}}{4 \pi} \frac{i}{a} 2 + \frac{\pi}{2} \hat{k}\) 

A particle of charge q and mass m moves in a circular orbit of radius r with angular speed ω. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

(1) ω and q

(2) ω, q and m

(3) q and m                     

(4) ω and m

A current \(I\) is carried by an elastic circular wire of length \(L\). It is placed in a uniform magnetic field \(B\) (out of paper) with its plane perpendicular to \(B'\text{s}\) direction. What will happen to the wire?

Wires 1 and 2 carrying currents $i_1$ and $i_2$ respectively are inclined at an angle $\theta$ to each other. What is the force on a small element dl of wire 2 at a distance of r from wire 1 (as shown in figure) due to the magnetic field of wire 1

(a) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \tan \theta$                              (b) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \sin \theta$

(c) $\frac{{\mu }_0}{2\mathrm{\pi r}}{i}_1{i}_{2}dl \cos \theta$                               (d) $\frac{{\mu }_0}{4\mathrm{\pi r}}{i}_1{i}_{2}dl \sin \theta$

A conducting loop carrying a current I is placed in a uniform magnetic field pointing into the plane of the paper as shown. The loop will have a tendency to

(1) Contract                                       

(2) Expand 

(3) Move towards +ve x -axis               

(4) Move towards -ve x -axis

A metallic block carrying current I is subjected to a uniform magnetic induction $\stackrel{\rightharpoondown }{B}$ as shown in the figure. The moving charges experience a force  $\stackrel{\rightharpoondown }{F}$ given by ........... which results in the lowering of the potential of the face ........ Assume the speed of the carriers to be v

(1) $eVB\hat{k}$ , ABCD                               

(2) $eVB\hat{k}$ , EFGH

(3) $-eVB\hat{k}$ , ABCD                             

(4) $-eVB\hat{k}$ , EFGH

Two insulated rings, one of slightly smaller diameter than the other are suspended along their common diameter as shown. Initially the planes of the rings are mutually perpendicular. When a steady current is set up in each of them

(1) The two rings rotate into a common plane

(2) The inner ring oscillates about its initial position

(3) The inner ring stays stationary while the outer one moves into the plane of the inner ring

(4) The outer ring stays stationary while the inner one moves into the plane of the outer ring

Two particles each of mass m and charge q are attached to the two ends of a light rigid rod of length 2R. The rod is rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod is:

1. $\frac{q}{2m}$                               

2. $\frac{q}{m}$

3. $\frac{2q}{m}$                              

4. $\frac{q}{\mathrm{\pi m}}$