First slide

Magnetism

Question

In figure, the magnetic needle has magnetic moment $6.7 x 10^{- 2} A m^{2}$ and moment of inertia $7.5 x 10^{- 6} k g m^{2}$ . It perform10 complete oscillations in 6.70s. What is the magnitude of the magnetic field? ………………. T.

Moderate

Solution

$G i v e n : M = 6.7 \times 10^{- 2} A m^{2}, I = 7.5 \times 10^{- 6} k g m^{2}, n = \frac{10}{6.7} H z$
$f r e q u e c y o f o s c i l l a t i o n = n = \frac{1}{2 π} \sqrt{\frac{M B}{I}} [w h e r e M = M a g n e t i c M o m e n t, I = M o m e n t o f I n e r t i a]$
$\Rightarrow B = \frac{4 π^{2} n^{2} I}{M} = \frac{4 π^{2} \times 10^{2} \times 7.5 \times 10^{- 6}}{6 . 7^{2} \times 6.7 \times 10^{- 2}} = 0.01 T$

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