Question

To measure the magnetic moment of a bar magnet, one may use

(a) a tangent galvanometer
(b) a deflection galvanometer if the earth's horizontal field is known
(c) an oscillation magnetometer if the earth's horizontal field is known
(d) both deflection and oscillation magnetometer if the earth's horizontal field is not known

Answer 1

(b) a deflection galvanometer if the earth's horizontal field is known
(c) an oscillation magnetometer if the earth's horizontal field is known
(d) both deflection and oscillation magnetometers if the earth's horizontal field is not known

Denial of (a):

Tangent galvanometer is an instrument used to measure electric current; it cannot be used to the measure magnetic moment of a bar magnet.

Justification of (b) and (c):

Deflection magnetometer is used to measure $\frac{M}{B_H}$ of a permanent bar magnet.
Similarly, oscillation magnetometer is used to measure M B_H of a bar magnet. So, if earth's horizontal field, B_H, is known, then the magnetic moment of a bar magnet, M, can be measured.

Justification of (d):

Using deflection and oscillation magnetometers, we can calculate $\frac{M}{B_H}$ and M B_H, respectively. Therefore, if we multiply the result obtained from both the instruments, then B_H cancels out as $\frac{M}{B_H}$$\times$ M B_H​ = M². Thus, the value of B_H is not required.
Therefore, we can use both deflection and oscillation magnetometers if the earth's horizontal field is not known.