A bar magnet of length l and magnetic dipole moment M is bent to form an arc which subtends an angle of $120°$ at centre. The new magnetic dipole moment will be

1.  $\frac{3\mathrm{M}}{2\mathrm{\pi }}$

2.  $\frac{3\sqrt{3}\mathrm{M}}{2\mathrm{\pi }}$

3.  $\frac{3\mathrm{M}}{\mathrm{\pi }}$

4.  $\frac{2\mathrm{M}}{\mathrm{\pi }}$

The unit of pole strength is:
1. \(\text{Am}^2\)
2. \(\text{Am}\)
3. \(\frac{\text{A}^2}{\text{m}}\)
4. \(\frac{\text{A}^2}{\text{m}^2}\)

A short magnetic dipole is placed at the origin with its dipole movement directed along the \(+x\text-\)axis. If magnetic field induction at a point \(P(r,0)\) is \(B\hat{i}\), the magnetic field induction at point \(Q(0,2r)\) will be:

The magnetic field at a point \(x\) on the axis of a small bar magnet is equal to the field at a point \(y\) on the equator of the same magnet. The ratio of the distances of \(x\) and \(y\) from the centre of the magnet is:
1. \(2^{-3}\)
2. \(2^{\frac{-1}{3}}\)
3. \(2^{3}\)
4. \(2^{\frac{1}{3}}\)

$1.<mspace\; width="1em"></mspace>\tau =niAB\cos \theta$
$2.<mspace\; width="1em"></mspace>\tau =niAB\sin \theta$
$3.<mspace\; width="1em"></mspace>\tau =niAB$
$4.<mspace\; width="1em"></mspace>None<mspace\; width="1em"></mspace>of<mspace\; width="1em"></mspace>the<mspace\; width="1em"></mspace>above$

Two short magnets with their axes horizontally perpendicular to the magnetic meridian are placed with their centres 40 cm east and 50 cm west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments  is

1. 4:5

2. 16:25

3. 64:125

4. 2:$\sqrt{5}$

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 magnet of magnetic moment M is situated with its axis along the direction of a magnetic field of strength B. The work done in rotating it by an angle of 180^o will be

1. -MB                        

2. +MB

3. 0                            

4. +2MB

A long magnetic needle of length \(2L\), magnetic moment \(M\) and pole strength \(m\) units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:
1. \(\frac{M}{2} , \frac{m}{2}\)
2. \(M , \frac{m}{2}\)
3. \(\frac{M}{2} , m\)
4. \(M, m\)

Two identical thin bar magnets each of length l and pole strength m are placed at the right angle to each other with the north pole of one touching south pole of the other. The magnetic moment of the system is :

1. ml

2. 2ml

3. $\sqrt{2}ml$

4. $\frac{1}{2}ml$