The frequency of oscillation of a small magnet in a magnetic field of induction 'B' is ' n '. If the frequency of oscillations of the same magnet in a field of induction 'X&#0

Question

The frequency of oscillation of a small magnet in a magnetic field of induction 'B' is ' n '. If the frequency of oscillations of the same magnet in a field of induction 'X' falls to ( 3 n ​ ) , the value of 'X' is

TestHub · Accepted Answer

The frequency of oscillation of a magnet in a magnetic field is given by

$n = \frac{1}{2 π} \frac{MB}{I}$

Since the same magnet is used, $M$ and $I$ are constant. Thus, $n \propto B$ , which implies $B \propto n^{2}$ .

Given $n_{1} = n$ at $B_{1} = B$ , and $n_{2} = \frac{n}{3}$ at $B_{2} = X$ .

$\frac{B _{1}}{B _{2}} = (\frac{n _{1}}{n _{2}})^{2}$

$\frac{B}{X} = (\frac{n}{n /3})^{2} = 3^{2} = 9$

$X = \frac{B}{9}$

Answer: $\frac{B}{9}$

Physics - Magnetism Question with Solution | TestHub

Options:

Doubts & Discussion