A short bar magnet of magnetic moment $5.25\times {10}^{-2} J T^{-1}$ is placed with its axis perpendicular to the earth’s field direction. At what distance from the center of the magnet, the resultant field is inclined at 45º with the earth’s field on its normal bisector.

(Magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.)

(1) 5.6 cm

(2) 6.3 cm

(3) 5.0 cm

(4) 6.5 cm

A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null–point (i.e., 14 cm) from the centre of the magnet?

(1) 0.54 G in the direction of the earth's magnetic field.

(2) 0.44 G in the opposite direction of the earth's magnetic field.

(3) 0.54 G in the opposite direction of the earth's magnetic field.

(4) 0.44 G in the direction of the earth's magnetic field.

A short bar magnet has a magnetic moment of $0.48 J T^{-1}.$ The direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on the equatorial lines (normal bisector) of the magnet is:

(1) 0.38 G along the N-S direction.

(2) 0.48 G along the N-S direction.

(3) 0.38 G along the S-N direction.

(4) 0.48 G along the S-N direction.

At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G. The magnitude of the earth’s field at the location is:

1. 0.16 G

2. 0.48 G

3. 0.32 G

4. 0.30 G

A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetizing current of 1.2 A?

(1) 3.27 T

(2) 2.56 T

(3) 1.05 T

(4) 4.48 T

A sample of paramagnetic salt contains $2.0\times {10}^{24}$ atomic dipoles each of dipole moment $1.5\times {10}^{-23} J T^{-1}.$ The sample is placed under a homogeneous magnetic field of 0.64 T and cooled to a temperature of 4.2 K. The degree of magnetic saturation achieved is equal to 15%. What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K?

(1) 9.219 J/T

(2) 11.105 J/T

(3) 10.336 J/T

(4) 8.287 J/T

A compass needle free to turn in a horizontal plane is placed at the centre of a circular coil of 30 turns and a radius of 12 cm. The coil is in a vertical plane making an angle of 45° with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. The horizontal component of the earth’s magnetic field at the location is:

(1) 0.299 G

(2) 0.497 G

(3) 0.388 G

(4) 0.535 G

A long straight horizontal cable carries a current of 2.5 A in the direction ${10}^0$ south of west to ${10}^0$ north of east. The magnetic meridian of the place happens to be 10° west of the geographic meridian. The earth’s magnetic field at the location is 0.33 G, and the angle of dip is zero. The neutral points lie on (ignore the thickness of the cable)? 

(1) a line parallel to the cable at a perpendicular distance of 1.5 cm above the plane of the paper.

(2) a line parallel to the cable at a perpendicular distance of 1.8 cm above the plane of the paper.

(3) a line parallel to the cable at a perpendicular distance of 0.7cm above the plane of the paper.

(4) none of these.

A closely wound solenoid of 800 turns and area of cross-section $2.5\times {10}^{-4} m^2$ carries a current of 3.0 A, is free to turn about the vertical direction and a uniform horizontal magnetic field of 0.25 T is applied, what is the magnitude of the torque on the solenoid when its axis makes an angle of ${30}^0$ with the direction of applied field?
 

$$\begin{gathered} \left(1\right) 7.5\times {10}^{-2} J \\ \left(2\right) 6.7\times {10}^{-3} J \\ \left(3\right) 7.5\times {10}^{-3} J \\ \left(4\right) 6.7\times {10}^{-2} J \end{gathered}$$

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 22° with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be 0.35 G. The magnitude of the earth’s magnetic field at the place is:

(1) 0.377 G

(2) 0.278 G

(3) 0.027 G

(4) 0.101 G