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 magnetic north pole. The neutral points are located at distance r from its centre. If magnet is rotated by 180^o, neutral point shall be obtained at distance

$$\begin{gathered} 1. 2\mathrm{r} \\ 2. \sqrt{2}\mathrm{r} \\ 3. 2^{-\frac{1}{3}}\mathrm{r} \\ 4. \frac{\mathrm{r}}{2\sqrt{2}} \end{gathered}$$

The unit of pole strength is

(1) $A{m}^2$

(2) Am

(3) $\frac{A^2}{m}$

(4) $\frac{A^2}{m^2}$

Two small bar magnets are placed in 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) $-\frac{B}{16}\hat{j}$

Oersted is a unit of :

(1) Dip

(2) Magnetic intensity

(3) Magnetic moment

(4) Pole strength

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