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

Each atom of an iron bar $(5 cm \times 1 cm \times 1 cm)$ has a magnetic moment $1.8\times {10}^{-23} A{m}^2$ . Knowing that the density of iron is $7.78\times {10}^3 kg{m}^{-3}$ atomic weight is 56 and Avogadro's  number is $6.02\times {10}^{23}$the magnetic moment of the bar in the state of magnetic saturation will be

1. 4.75 Am²                  2. 5.74 Am²

3. 7.54 Am²                  4. 75.4 Am²

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. 

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 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 

1. zero

2. directed along OP

3. directed along PO

4. directed perpendicular to the plane of the paper

The variation of the intensity of magnetisation (I) with respect to the magnetising field (H) in a diamagnetic substance is described by the graph

1. OD                            2. OC

3. OB                            4. OA

The magnet of a vibration magnetometer is heated so as to reduce its magnetic moment by 19%. By doing this the periodic time of the magnetometer will

1. Increase by 19%       2. Decrease by 19%

3. Increase by 11%       4. Decrease by 21%

A straight wire carrying a current i is turned into a circular loop. If the magnitude of the magnetic moment associated with it in M.K.S. unit is M, the length of wire will be

1. $4\mathrm{\pi iM}$                          2. $\sqrt{\frac{4\mathrm{\pi M}}{i}}$

3. $\sqrt{\frac{4\mathrm{\pi i}}{M}}$                        4. $\frac{M\mathrm{\pi }}{4i}$

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. $\frac{2W}{\sqrt{3}}$

A magnet of magnetic moment M oscillating freely in earth's horizontal magnetic field makes n oscillations per minute. If the magnetic moment is quadrupled and the earth's field is doubled, the number of oscillations made per minute would be

1. $\frac{n}{2\sqrt{2}}$                         2. $\frac{n}{\sqrt{2}}$

3. $2\sqrt{2}n$                        4. $\sqrt{2}n$