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:
1. \(2T\)
2. \(\frac{T}{2}\)
3. \(\frac{2}{T}\)
4. \(T\)

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:

Due to a small magnet, the intensity at a distance \(x\) in the end-on position is \(9~\text{gauss}\). What will be the intensity at a distance \(\frac{x}{2}\) on equatorial position?
1. \(9~\text{gauss}\)
2. \(4~\text{gauss}\)
3. \(36~\text{gauss}\)
4. \(4.5~\text{gauss}\)

Figure shows two small identical magnetic dipoles \(a\) and \(b\) of magnetic moments \(M\) each, placed at a separation \(2d\), with their axes perpendicular to each other. The magnetic field at the point \(P\) midway between the dipoles is:

1. \(\frac{2 \mu_{0} M}{4 \pi d^{3}}\)

2. \(\frac{\mu_{0} M}{4 \pi d^{3}}\)

3. zero

4. \(\frac{\sqrt{5}\mu_{0} M}{4\pi d^{3}}\)

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

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.

A vibration magnetometer placed in a magnetic meridian has a small bar magnet. The magnet executes oscillations with a time period of 2 s in the earth's horizontal magnetic field of 24 $\mu$T. When a horizontal field of 18 $\mu$T is produced opposite to the earth's field by placing a current-carrying wire, the new time period of the magnet will be:

1. 1 s

2. 2 s

3. 3 s

4. 4 s

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.

A Gaussian surface is drawn enclosing the N-pole of a bar magnet. The net magnetic flux through the Gaussian surface will be:
(pole strength of N-pole is treated as positive and S-pole as negative)