A magnet of magnetic moment 20 C.G.S. units are freely suspended in a uniform magnetic field of intensity 0.3 C.G.S. units. The amount of work done in deflecting it by an angle of ${30}^o$ in C.G.S. units is

1. 6

2. $3\sqrt{3}$

3. $3(2-\sqrt{3})$

4. 3

The magnetic field due to a short magnet at a point on its axis at a distance X cm from the middle point of the magnet is 200 Gauss. The magnetic field at a point on the neutral axis at a distance of X cm from the middle of the magnet is:

1. 100 Gauss

2. 400 Gauss

3. 50 Gauss

4. 200 Gauss

If a bar magnet of magnetic moment M is freely suspended in a uniform magnetic field of strength B, the work done in rotating the magnet through an angle is

1. $MB(1-\sin \theta )$

2. $MB\sin \theta$

3. $MB\cos \theta$

4. $MB(1-\cos \theta )$

A bar magnet of magnetic moment 10⁴J/T is free to rotate in a horizontal plane. The work done in rotating the magnet slowly from a direction parallel to a horizontal magnetic field of 4×10^–5 T to a direction 60° from the field will be

1. 0.2 J                          2. 2.0 J

3. 4.18 J                        4. 2 × 10² J

A magnet of magnetic moment $50\widehat{i<mspace\; width="1em"></mspace>}A-m^2$ is placed along the x-axis in a magnetic field $\overrightarrow{B}=(0.5\hat{i}+3.0\hat{j})T$. The torque acting on the magnet is

1. 175 $\hat{k}$ N-m

2. 150 $\hat{k}$ N-m

3. 75 $\hat{k}$ N-m

4. 25$\sqrt{37}$ $\hat{k}$ N-m