Two bar magnets with magnetic moments 2 M and M are fastened together at right angles to each other at their centres to form a crossed system, which can rotate freely about a vertical axis through the centre. The crossed system sets in earth’s magnetic field with magnet having magnetic moment 2M making an angle $\theta$ with the magnetic meridian such that

(a) $\theta ={\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$            (b) $\theta ={\tan }^{-1}\left(\sqrt{3}\right)$

(c) $\theta ={\tan }^{-1}\left(\frac{1}{2}\right)$               (d) $\theta ={\tan }^{-1}\left(\frac{3}{4}\right)$

The angle of dip at a certain place is 30^o. If the horizontal component of the earth’s magnetic field is H, the intensity of the total magnetic field is

1. $\frac{H}{2}$                            2. $\frac{2H}{\sqrt{3}}$

3. $H\sqrt{2}$                         4. $H\sqrt{3}$

A magnet is suspended in such a way that it oscillates in the horizontal plane. It makes 20 oscillations per minute at a place where dip angle is 30^o and 15 oscillations per minute at a place where dip angle is 60^o. The ratio of total earth's magnetic field at the two places is

1. $3\sqrt{3}:8$                      2. $16:9\sqrt{3}$

3. 4:9                           4. $2\sqrt{3}:9$

A bar magnet A of magnetic moment M_A is found to oscillate at a frequency twice that of magnet B having identical size as magnet A, of magnetic moment M_B when placed in a vibrating magneto-meter. We may say that

(1) $M_A=2M_B$                 

(2) M_A = 8M_B

(3) M_A = 4M_B                 

(4) M_B = 8M_A

A magnet of magnetic moment M oscillating freely in earth's horizontal magnetic field makes n oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled, the number of oscillations made per minute would be

1. $\frac{n}{2\sqrt{2}}$                         2. $\frac{n}{\sqrt{2}}$

3. $2\sqrt{2}n$                        4. $\sqrt{2}n$

Two identical short bar magnets, each having magnetic moment M, are placed a distance of 2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

(a)  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{2}\right) \frac{M}{d^3}$                (b)  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{3}\right) \frac{M}{d^3}$

(c)  $\left(\frac{2{\mu }_0}{4\mathrm{\pi }}\right)\frac{M}{d^3}$                 (d) $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{5}\right) \frac{M}{d^3}$

The basic magnetization curve for a ferromagnetic material is shown in the figure. Then, the value of relative permeability is highest for the point :

1. P         

2. Q

3. R         

4. S

A superconductor exhibits perfect:
1. Ferrimagnetism
2. Ferromagnetism
3. Paramagnetism             
4. Diamagnetism

Among the following properties describing diamagnetism identify  the property that is wrongly stated

1. Diamagnetic material do not have permanent magnetic moment

2. Diamagnetism is explained in terms of electromagnetic induction

3. Diamagnetic materials have a small positive susceptibility

4. The magnetic moment of individual electrons neutralize each other

If a magnet is suspended at an angle 30^o to the magnetic meridian, it makes an angle of 45^o with the horizontal. The real dip is

(a)${\tan }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

(b)${\tan }^{-1}\left(\sqrt{3}\right)$

(c)${\tan }^{-1}\left(\sqrt{\frac{3}{2}}\right)$

(d)${\tan }^{-1}\left(\frac{2}{\sqrt{3}}\right)$