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

A small bar magnet is placed with its north pole facing the magnetic north pole. The neutral points are located at a distance r from its centre. If the magnet is rotated by 180^o, the neutral point shall be obtained at a distance of:
1. \(2r\)
2. \(\sqrt{2}r\)
3. \(2^{\frac{1}{3}}r\)
4. \(\frac{r}{2\sqrt{2}}\)

The unit of pole strength is:

1. $A{m}^2$

2. Am

3. $\frac{A^2}{m}$

4. $\frac{A^2}{m^2}$

Magnetic field lines

1. Cannot intersect

2. Are always closed curves

3. Can pass through vacuum

4. All of these

Two small bar magnets are placed in the air at a distance r apart. The magnetic force between them is proportional to:

(1) $r^2$

(2) $r^{-2}$

(3) $r^{-3}$

(4) $r^{-4}$

A short magnetic dipole is placed at the origin with its dipole movement directed along the +x-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:

1. \(-\frac{B}{16}\hat{i}\)

2. \(-\frac{B}{8}\hat{j}\)

3. \(\frac{B}{16}\hat{j}\)

4. \(-\frac{B}{16}\hat{j}\)

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. $2^{\raisebox{1ex}{$-1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

3. $2^3$

4. $2^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

A magnet of magnetic moment 20 C.G.S. units are freely suspended in a uniform magnetic field of intensity 0.3 C.G.S. units. The amount of work done in deflecting it by an angle of ${30}^o$ in C.G.S. units is
(1) 6

(2) $3\sqrt{3}$

(3) $3(2-\sqrt{3})$

(4) 3

The magnetic field due to a short magnet at a point on its axis at a distance X cm from the middle point of the magnet is 200 Gauss. The magnetic field at a point on the neutral axis at a distance of X cm from the middle of the magnet is:

1. 100 Gauss

2. 400 Gauss

3. 50 Gauss

4. 200 Gauss

A sensitive magnetic instrument can be shielded very effectively from outside magnetic fields by placing it inside a box of
1. Teak wood
2. Plastic material
3. Soft iron of high permeability
4. A metal of high conductivity