A particle having a mass of ${10}^{-2}$ $\mathrm{kg}$ $$carries a charge of $5\times {10}^{-8}$ $\mathrm{C}.$ The particle is given an initial horizontal velocity of ${10}^5$ ${\mathrm{ms}}^{-1}$ in the presence of an electric field $\overrightarrow{\mathbf{E}}$ and magnetic field $\overrightarrow{\mathbf{B}}$. How can we keep the particles moving in a horizontal direction?

a.	$\overrightarrow{\mathbf{B}}$ should be perpendicular to the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.
b.	Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ should be along the direction of velocity.
c.	Both $\overrightarrow{\mathbf{B}}$ and $\overrightarrow{\mathbf{E}}$ are mutually perpendicular and perpendicular to the direction of velocity.
d.	$\overrightarrow{\mathbf{B}}$ should be along the direction of velocity and $\overrightarrow{\mathbf{E}}$ should be perpendicular to the direction of velocity.

Which one of the following pairs of statements are possible?
1. a and c 
2. c and d
3. b and c
4. b and d

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. What is the ratio of the magnitudes of the magnetic moment of the system and its angular momentum about the centre of the rod?

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

2. $\frac{q}{m}$

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

4. $\frac{q}{\mathrm{\pi m}}$ 

By which relation is the deflection of the coil θ related to the electrical current i in a moving coil galvanometer?

1. $i\propto \tan \theta$                 

2. $i\propto \theta$ 

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

4. $i\propto \sqrt{\theta }$ 

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 ω, 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. $\frac{1}{2}Q{\omega }^{2}R$

A long wire A carries a current of 10 A. Another long wire B, which is parallel to A and separated by 0.1 m from A, carries a current of 5 A, in the opposite direction to that in A. What is the magnitude and nature of the force experienced per unit length of B?
$({\mu }_0=4\mathrm{\pi }\times {10}^{-7}weber/amp-\mathrm{m})$
 

If the magnetic field at the centre of the circular coil is B₀, then what is the distance on its axis from the centre of the coil where  \(B_x=\frac{B_0}{8}~?\)
(R= radius of the coil)

What happens when the number of turns in a galvanometer is doubled?

The two parts of the loop are circles of radii 2a and a, respectively, and carry the same current i as shown in the given figure. What is the magnitude of the dipole moment of the current loop?

1. $5{\mathrm{\pi a}}^2$ $\mathrm{i}$

2. $4{\mathrm{\pi a}}^2$ $\mathrm{i}$

3. $3{\mathrm{\pi a}}^2$ $\mathrm{i}$

4. Zero

What is the magnetic moment of the following current loop?
 
1. $24$ $A{m}^2$

2. $12$ $A{m}^2$

3. $6$ $A{m}^2$

4. Zero

As indicated, a long, straight conductor XY carrying a current i₁ is placed antiparallel to a conductor AB of length l carrying a current i₂. How much of a force is acting on AB?

1. ${\mu }_0{i}_1{i}_2$

2.  $\frac{{\mu }_0{i}_1{i}_2}{\mathrm{\pi }}$

3. $\frac{{\mu }_0{i}_1{i}_2}{2\mathrm{\pi }}$

4. $2{\mu }_0{i}_1{i}_2$