At a certain place, the horizontal component B₀ and the vertical component V₀ of the earth's magnetic field are equal in magnitude. The total intensity at the place will be

1. $B_0$                            2. $B_0^2$

3. $2B_0$                          4. $\sqrt{2}{B}_0$

If ${\varphi }_1$ and ${\varphi }_2$ be the angles of dip observed in two vertical planes at right angles to each other and $\varphi$ be the true angle of dip, then

1. ${\cos }^2\varphi ={\cos }^2{\varphi }_1+{\cos }^2{\varphi }_2$

2. ${\sec }^2\varphi ={\sec }^2{\varphi }_1+{\sec }^2{\varphi }_2$

3. ${\tan }^2\varphi ={\tan }^2{\varphi }_1+{\tan }^2{\varphi }_2$

4. ${\cot }^2\varphi ={\cot }^2{\varphi }_1+{\cot }^2{\varphi }_2$

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. $H\sqrt{3}$

Magnetic field lines

1. Cannot intersect

2. Are always closed curves

3. Can pass through vacuum

4. All of these

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. $\frac{1}{2}ml$

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

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. $2\sqrt{3}:9$

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

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

1. 

2. 

3. 

4. 

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)