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.

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. 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

Two tangent galvanometers having coils of the same radius are connected in series. A current flowing in them produces deflections of 60° and 45° respectively. The ratio of the number of turns in the coils is

1. 4/3                 2. $\frac{\sqrt{3}+1}{1}$

3. $\frac{\sqrt{3}+1}{\sqrt{3}-1}$          4. $\frac{\sqrt{3}}{1}$

The time period of oscillation of a bar magnet suspended horizontally along the magnetic meridian is T₀. If this magnet is replaced by another magnet of the same size and pole strength but with double the mass, the new time period will be

(1) $\frac{T_0}{2}$                           

(2) $\frac{T_0}{\sqrt{2}}$

(3) $\sqrt{2}{T}_0$                        

(4) 2T₀

A thin rectangular magnet suspended freely has a period of oscillation equal to T. Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate freely in the same field. If its period of oscillation is T', then ratio T'/T is:

1. 1/4

2. $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2\sqrt{2}$}\right.$

3. 1/2

4. 2

Two identical short bar magnets, each having magnetic moment M, are placed a distance of 2d apart with axes perpendicular to each other in a horizontal plane. The magnetic induction at a point midway between them is

(a)  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{2}\right) \frac{M}{d^3}$                (b)  $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{3}\right) \frac{M}{d^3}$

(c)  $\left(\frac{2{\mu }_0}{4\mathrm{\pi }}\right)\frac{M}{d^3}$                 (d) $\frac{{\mu }_0}{4\mathrm{\pi }}\left(\sqrt{5}\right) \frac{M}{d^3}$