Two equal bar magnets are kept as shown in the figure. The direction of the resultant magnetic field, indicated by arrowhead at the point \(P\) is: (approximately)

          

1.		2.
3.		4.

If a magnetic needle is made to vibrate in uniform field \(H\), then its time period is \(T\). If it vibrates in the field of intensity \(4H\), its time period will be:

Magnets \(A\) and \(B\) are geometrically similar but the magnetic moment of \(A\) is twice that of \(B\). If \(T_1\) and \(T_2\) be the time periods of the oscillation when their like poles and unlike poles are kept together respectively, then \(\frac{T_1}{T_2}\) will be:
1. \(\frac{1}{3}\)
2. \(\frac{1}{2}\)
3. \(\frac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)

A thin rectangular magnet suspended freely has a period of oscillation equal to \(T\). Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is \(T'\), then ratio \(\frac{T'}{T}\) is:
1. \(\frac{1}{4}\)
2. \(\frac{1}{2\sqrt{2}}\)
3. \(\frac{1}{2}\)
4. \(2\)

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. \(-0.064~\text J\) 

Two identical bar magnets are fixed with their centres at a distance \(d\) apart. A stationary charge \(Q\) is placed at \(P\) in between the gap of the two magnets at a distance \(D\) from the centre \(O\) as shown in the figure.

The unit of pole strength is:
1. \(\text{Am}^2\)
2. \(\text{Am}\)
3. \(\frac{\text{A}^2}{\text{m}}\)
4. \(\frac{\text{A}^2}{\text{m}^2}\)