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 a dipole moment $M,$ are placed at the origin—oriented along the $x\text-$axis, the $y\text-$axis, and the $z\text-$axis respectively. The net magnetic moment of the dipoles has the magnitude:
1. $3M$
2. $\sqrt2M$
3. $\sqrt3M$
4. 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. $\frac{\mu_{\mathrm{0}}}{4 \pi} \frac{\mathrm{2M}}{\mathrm{d}^{3}}$