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:

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. $r^{-4}$

Magnetic field lines

1. Cannot intersect

2. Are always closed curves

3. Can pass through vacuum

4. All of these

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 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. $\frac{r}{2\sqrt{2}}$

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 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. $2^{\frac{1}{3}}$

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