A small bar magnet is placed with its north pole facing the magnetic north pole. The neutral points are located at a distance r from its centre. If the magnet is rotated by 180^o, the neutral point shall be obtained at a distance of:
1. \(2r\)
2. \(\sqrt{2}r\)
3. \(2^{\frac{1}{3}}r\)
4. \(\frac{r}{2\sqrt{2}}\)

A neutral point is obtained at the centre of a vertical circular coil carrying current. The angle between the plane of the coil and the magnetic meridian is :

1. 0                           2. 45°

3. 60°                       4. 90°

A dip needle in a plane perpendicular to magnetic meridian will remain

1. Vertical

2. Horizontal

3. In any direction

4. At an angle of dip to the horizontal

If the angles of dip at two places are 30^o and 45^o respectively, then the ratio of horizontal  components of earth's magnetic field at the two places will be:
(Assume net magnetic field to be equal at the two places)

1. √3 : √2

2. 1 : √2

3. 1 : √3

4. 1 : 2

A line passing through places having zero value of magnetic dip is called

1. Isoclinic line            

2. Agonic line

3. Isogonic line            

4. Aclinic line

The earth's magnetic field at a certain place has a horizontal component 0.3 Gauss and the total strength 0.5 Gauss. The angle of dip is

1. ${\tan }^{-1}\left(\frac{3}{4}\right)$                     

2. ${\sin }^{-1}\left(\frac{3}{4}\right)$

3. ${\tan }^{-1}\left(\frac{4}{3}\right)$                     

4. ${\sin }^{-1}\left(\frac{3}{5}\right)$

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. $\sqrt{2}{B}_0$

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

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

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

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. $2\sqrt{3}:9$