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

1.	end-on position	2.	broadside-on position
3.	both	4.	none

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

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

Which of the following pairs has quantities of the same dimensions?

Choose the correct option from the given ones: 
1. (a) and (b) only
2. (b) and (c) only
3. (c) and (d) only
4. (a) and (d) only

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

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