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

(1) $co{t}^2\theta =co{t}^2{\theta }_1+co{t}^2{\theta }_2$

(2) ${\tan }^2\theta ={\tan }^2{\theta }_1+ {\tan }^2{\theta }_2$

(3) $co{t}^2\theta =co{t}^2{\theta }_1-{\tan }^2{\theta }_2$

(4) ${\tan }^2\theta ={\tan }^2{\theta }_1-{\tan }^2{\theta }_2$

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by ${60}^{\circ }$ is W. Now the torque required to keep the magnet in this new position is:

1. $\frac{W}{\sqrt{3}}$ 
2. $\sqrt{3}W$
3. $\frac{\sqrt{3}W}{2}$ 
4. $\frac{2W}{\sqrt{3}}$

The magnetic susceptibility is negative for

1. paramagnetic material only

2. ferromagnetic material only

3. paramagnetic and ferromagnetic materials

4. diamagnetic material only

The following figures show the arrangement of bar magnets in different configurations. Each magnet has magnetic dipole. Which configuration has the highest net magnetic dipole moment? 

1.		2.
3.		4.

A compass needle which is allowed to move in a horizontal plane is taken to a geomagnetic pole.It

(1) will become rigid showing no movement

(2) will stay in any position

(3) will stay in north-south direction only

(4) will stay in east-west direction only

A magnetic needle suspended parallel to a magnetic field requires $\sqrt{3}$ J of work to turn it through $60°$. The torque needed to maintain the needle in this position will be

1. $2\sqrt{3}$J                     

2. 3 J

3. $\sqrt{3}$ J                       

4. $\frac{3}{2}$ J

There are four light-weight-rod samples; A, B, C, D separately suspended by threads. A bar magnet is slowly brought near each sample and the following observations are noted:

(i) A is feebly repelled 

(ii) B is feebly attracted

(iii) C is strongly attracted

(iv) D remains unaffected

Which one of the following is true?

1. C is of a diamagnetic material

2. D is of a ferromagnetic material

3. A is of a non-magnetic material

4. B is of a paramagnetic material

A short bar magnet of magnetic moment 0.4 JT^–1 is placed in a uniform magnetic field of 0.16 T. The magnet is in stable equilibrium when the potential energy is:

1. – 0.64 J

2. zero

3. – 0.82 J

4. – 0.064 J

Two identical bar magnets are fixed with their centres at a distance d apart. A stationary charge Q is placed at P in between the gap of the two magnets at a distance D from the centre O as shown in the figure.

The force on the charge Q is:

If a diamagnetic substance is brought near the north or the south pole of a bar magnet, it is

1. repelled by both the poles

2. repelled by the north pole and attracted by the south pole

3. attracted by the north pole and repelled by the south pole

4. attracted by both the poles