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

                   

1. $\frac{2{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{4-{\pi }^2}$                                 
2. $\frac{{\mu }_{0}i}{3\mathrm{\pi a}}\sqrt{4+{\pi }^2}$

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

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. The net magnetic field at centre will be $\left(\theta =\frac{\pi }{n}\right)$

(a) $\frac{{\mu }_{o}i}{2\mathrm{\pi a}}\tan \frac{\mathrm{\pi }}{n}$                                                (b) $\frac{{\mu }_{0}ni}{2\mathrm{\pi a}}\tan \frac{\mathrm{\pi }}{n}$

(c)$\frac{2}{\mathrm{\pi }}\frac{ni}{a}{\mu }_0\tan \frac{\mathrm{\pi }}{n}$                                             (d) $\frac{ni}{2a}{\mu }_0\tan \frac{\mathrm{\pi }}{n}$

An elastic circular wire of length L carries a current I. It is placed in a uniform magnetic field $\overrightarrow{B}$ (out of paper) such that its plane is perpendicular to the direction of $\overrightarrow{B}$ . The wire will experience

(1) No force                           

(2) A stretching force

(3) A compressive force           

(4) A torque

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 current-carrying loop is placed in a uniform magnetic field in four different orientations, \(\mathrm{I, II, III} \) & \( \mathrm{IV.}\) The decreasing order of potential energy is :
              

I.
II.
III.
IV.

1. \(\mathrm{I > III > II > IV }     \)
2. \(\mathrm{I > II >III > IV}\)
3. \(\mathrm{I > IV > II > III   }\)
4. \(\mathrm{III > IV > I > II}\)

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

A charge \(Q\) is uniformly distributed on a ring of radius \(R\) made of an insulating material. If the ring rotates about the axis passing through its centre and normal to the plane of the ring with constant angular speed \(\omega\), then what will be the magnitude of the magnetic moment of the ring?
1. \(Q \omega R^{2}\)
2. \(\frac{1}{2} Q \omega R^{2}\)
3. \(Q \omega^{2} R\)
4. \(\frac{1}{2} Q\omega^{2} R\)$$

What is the net force on the square coil ?

(1) $25\times {10}^{-7}N$ 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