$1. \tau =niAB\cos \theta$
$2. \tau =niAB\sin \theta$
$3. \tau =niAB$
$4. None of the above$

Two short magnets with their axes horizontally perpendicular to the magnetic meridian are placed with their centres 40 cm east and 50 cm west of the magnetic needle. If the needle remains undeflected, the ratio of their magnetic moments  is

1. 4:5

2. 16:25

3. 64:125

4. 2:$\sqrt{5}$

Two small bar magnets are placed in a line with like poles facing each other at a certain distance d apart. If the length of each magnet is negligible as compared to d, the force between them will be inversely proportional to

1. d

2. d²

3. $\frac{1}{d^2}$

4. $d^4$

A magnet of magnetic moment M is situated with its axis along the direction of a magnetic field of strength B. The work done in rotating it by an angle of 180^o will be

1. -MB                        

2. +MB

3. 0                            

4. +2MB

A long magnetic needle of length \(2L\), magnetic moment \(M\) and pole strength \(m\) units is broken into two pieces at the middle. The magnetic moment and pole strength of each piece will be:
1. \(\frac{M}{2} , \frac{m}{2}\)
2. \(M , \frac{m}{2}\)
3. \(\frac{M}{2} , m\)
4. \(M, m\)

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 the resultant magnetic field, indicated by arrowhead at the point \(P\) is: (approximately)

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

The number of turns and radius of cross-section of the coil of a tangent galvanometer is doubled. The reduction factor K will be
1. K                              2. 2K
3. 4K                            4. K/4