Consider a magnetic dipole kept in the north-south direction. Let P₁, P₂ Q₁, Q₂ be four points at the same distance from the dipole towards the north, south, east and west of the dipole respectively. The directions of the magnetic field due to the dipole are the same at:
 

a.	P1 and P2
b.	Q1 and Q2
c.	P1 and Q1
d.	P2 and Q2

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: 
1. (a), (b)
2. (b), (c)
3. (c), (d)
4. (a), (d)

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

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

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. \(\text{zero}\)

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