The following figures show the arrangement of bar magnet in different configurations. Each magnet has magnetic dipole moment m. Which configuration has the highest net magnetic dipole moment?
(i) (ii) (iii) (iv)

1. (i)

2. (ii)

3. (iii)

4. (iv)

Two short magnets of equal dipole moments M are fastened perpendicularly at their centres (figure). The magnitude of the magnetic field at a distance d from the centre on the bisector of the right angle is :

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

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

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

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

Time period for a magnet is T. If it is divided in four equal parts along its axis and perpendicular to its axis as shown then time period for each part will be

1. 4T

2. T/4

3. T/2

4. T

The variation of magnetic susceptibility $\left(\chi \right)$ with temperature for a diamagnetic substance is best represented by

1. 

2. 

3. 

4. 

1. Intersect at the neutral point

2. Intersect near the poles of the magnet

3. Intersect on the equatorial axis of the magnet

4. Do not intersect at all

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. $2\sqrt{3}:9$

The time period of oscillation of a freely suspended bar magnet with usual notations is given by

1. $T=2\mathrm{\pi }\sqrt{\frac{\mathrm{I}}{{\mathrm{MB}}_{\mathrm{H}}}}$

2.  $T=2\mathrm{\pi }\sqrt{\frac{M{B}_H}{I}}$

3. $T=2\sqrt{\frac{\mathrm{I}}{{\mathrm{MB}}_{\mathrm{H}}}}$

4. $T=2\mathrm{\pi }\sqrt{\frac{B_H}{MI}}$

Two identical thin bar magnets each of length l and pole strength m are placed at the right angle to each other with the north pole of one touching south pole of the other. The magnetic moment of the system is :

1. ml

2. 2ml

3. $\sqrt{2}ml$

4. $\frac{1}{2}ml$

Magnetic field lines

1. Cannot intersect

2. Are always closed curves

3. Can pass through vacuum

4. All of these

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. $H\sqrt{3}$