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: