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. \(4.5~\text{gauss}\)

A long magnetic needle of length \(2L\), magnetic moment \(M\) and pole strength \(m\) units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:
1. \(\frac{M}{2} , \frac{m}{2}\)
2. \(M , \frac{m}{2}\)
3. \(\frac{M}{2} , m\)
4. \(M, m\)

The magnetic moment of a bar magnet of length \(L\) and area of cross-section \(A\) is \(M\). If the magnet is cut into four identical parts each of length \(L\) and area of cross-section \(\frac{A}{4}\), then magnetic moment of each part is:

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

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