A circular loop carrying a current is replaced by an equivalent magnetic dipole. A point on the axis of the loop is in: 

Choose the correct option: 
1. (a), (b) 
2. (b), (c) 
3. (c), (d) 
4. (a), (d) 

When a bar magnet is rotated from its position parallel to the external magnetic field \(B=10^{-3}\) T to a direction opposite to the field (anti-parallel), the work done is \(3\) J.
Then, the maximum torque experienced by this magnet in this field is:
1. \(3\times10^{-3}\) N-m
2. \(3\times10^{3}\) N-m
3. \(6\) N-m
4. \(1.5\) N-m

Three identical bar magnets, each having dipole moment \(M,\) are placed at the origin — oriented along the x-axis, the y-axis and the z-axis respectively. The net magnetic moment of the dipoles has the magnitude:
1. \(3~M\)

2. \(\sqrt2~M\)

3. \(\sqrt3~M\)

4. \(\text{zero}\)

The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole. Which configuration has the highest net magnetic dipole moment?

1.		2.
3.		4.

1. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{M}}{\mathrm{d}^{3}}\)
2. \(\frac{\mu_{0}}{4 \pi} \frac{\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
3. \(\frac{\mu_{0}}{4 \pi} \frac{2\sqrt{2} \mathrm{M}}{\mathrm{d}^{3}}\)
4. \(\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{2M}}{\mathrm{d}^{3}}\)