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. $\frac{1}{2}ml$

Two equal bar magnets are kept as shown in the figure. The direction of resultant magnetic field, indicated by arrow head at the point P is (approximately)

1. 

2. 

3. 

4. 

Two similar bar magnets P and Q, each of magnetic moment M, are taken. If P is cut along its axial line and Q is cut along its equatorial line, all the four pieces obtained have

1. Equal pole strength          2. Magnetic moment M/4

3. Magnetic moment M/2      4. Magnetic moment M

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

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. B₀

2. B₀²

3. 2B₀                         

4. √2B₀

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