If a bar magnet is kept on a horizontal plane with N-pole of bar magnet facing geographic N-pole and S-pole of bar magnet facing geographic S-pole, then the number of neutral points is:

The correct direction of the magnetic field in the given figures is shown by:

1.		2.
3.		4.

A current-carrying loop is placed in a uniform magnetic field in four different orientations, I, II, III & IV. The decreasing order of potential energy is:

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by $60^{\circ}$ is $W$. Now the torque required to keep the magnet in this new position is:
1. $\frac{W}{\sqrt{3}}$ 
2. $\sqrt{3} W$
3. $\frac{\sqrt{3} W}{2}$ 
4. $\frac{2 W}{\sqrt{3}}$

A short bar magnet of magnetic moment $0.4~\text {J/T}$ is placed in a uniform magnetic field of $0.16~\text T.$ The magnet is in stable equilibrium when the potential energy is:
1. $0.064~\text J$
2. zero
3. $-0.082~\text J$ 
4. $-0.064~\text J$ 

A bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment 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. $2^{\frac{1}{3}}$

Two magnets $A$ and $B$ are identical and these are arranged as shown in the figure. Their length is negligible in comparison to the separation between them. A magnetic needle is placed between the magnets at point $P$ which gets deflected through an angle $\theta$ under the influence of magnets. The ratio of distance $d_1$ and $d_2$ will be:
   
1. $(2\tan\theta)^{\frac{1}{3}}$
2. $(2\tan\theta)^{\frac{-1}{3}}$
3. $(2\cot\theta)^{\frac{1}{3}}$
4. $(2\cot\theta)^{\frac{-1}{3}}$

Two short magnets of equal dipole moments $M$ are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance $d$ from the centre on the bisector of the right angle is: