Question

The earth magnet field BH,if the frequency of oscillation of a magnetic needle is n, than what is relashion between BH and n

Answer 1

Answer:$n^{2} \propto B$

Explanation: We know the time period of oscillation of magnetic needle in uniform earth's magnetic field

$T = 2\pi \sqrt{\dfrac{I}{MB}}$

Where,

I = moment of inertia of needle about its axis

M = Magnetic moment

B = Magnetic field of the earth

We know the relation between frequency of oscillation and time period.

$n = \dfrac{1}{T}$.....(I)

Now, put the value of T in equation (I)

$n = \dfrac{1}{2\pi}\sqrt{\dfrac{MB}{I}}$

$n^{2} \propto B$

Hence, the square of the  frequency of oscillation of a magnetic needle is direct proportional of the magnetic field of earth.