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. T/2

3. 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. $A{m}^2$

2. Am

3. $\frac{A^2}{m}$

4. $\frac{A^2}{m^2}$

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. $\frac{2{\mathrm{\mu }}_0\mathrm{M}}{4{\mathrm{\pi d}}^3}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{M}}{4{\mathrm{\pi d}}^3}$

3. Zero

4. $\frac{\sqrt{5}{\mathrm{\mu }}_0\mathrm{M}}{4{\mathrm{\pi d}}^3}$