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(a) Show that the time period (T) of oscillations of a freely suspended magnetic dipole of magnetic moment (m) in a uniform magnetic field (B) is given by $T=2\pi \sqrt{\frac{I}{mB}}$ , where I is a moment of inertia of the magnetic dipole.

(b) Identify the following magnetic materials :

(i) A material having susceptibility $(\chi_{m})=-0.00015$ .

(ii) A material having susceptibility $(\chi_{m})=10^{-5}$ .

Answers (1)

(a) $\tau =\vec{M}\times \vec{B}$

$\tau =MB\sin \theta$

For small ang $\theta$ , we have

$\tau =MB\theta$

$\alpha=\frac{d^2\theta}{dt^2}$

$\alpha=\left ( \frac{MB}{I} \right )\theta$

Now, compairing with angular SHM, we get

$\omega ^{2}=\frac{mB}{I}$

$T=\frac{2\pi }{\omega }=2\pi \sqrt{\frac{I}{mB}}$

Where m=magnetic moment

I= moment of inertia

B= magnetic field intensity

(b) Such that,

$\because x_{m}< 0, diamagnetic$

$\because x_{m}> 0, paramagnetic$

$\because x_{m}> > 1, 1ferromagnetic$

Where, $x_{m}$ is the magnetic susceptibility

(i) $x_{m}=-0.00015$

hence, it is diamagnetic

(ii) $x_{m}=10^{-5}> 0$

hence, it is paramagnetic

Posted by

Safeer PP

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