Question

In earth' magnetic field Bh, if the frequency of oscillation of a magnetic needle is n, then-​

Answer 1

answer : $n^2\propto B_h$

explanation : here needle is oscillate in the earth magnetic field.

so, time period of oscillation of needle in uniform earth's magnetic field is given by, $T=2\pi\sqrt{\frac{I}{MB_h}}$ ......(1)

where I is moment of inertia of needle about its axis , M is the magnetic moment of needle. and $B_h$ is earth's magnetic field.

now, relation between time period and frequency is given by, $n=\frac{1}{T}$......(2)

so, frequency of needle in uniform earth's magnetic field is given by, $n=\frac{1}{2\pi}\sqrt{\frac{MB}{I}}$

[ from equations (1) and (2), ]

here it is clear that, $n\propto\sqrt{B_h}$

hence,$n^2\propto B_h$