Motional EMF

Question

A metallic rod of mass per unit length 0.5 kg ${m}^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of ${30}^{0}$ with the horizontal. The rod is not allowed to slide down by flowing a current through it when a magnetic field of induction 0.25 *T* is acting on it in the vertical direction. The current flowing in the rod to keep it stationary is

Moderate

Solution

Mass per unit length of a metallic rod

$\frac{m}{l}=0.5\mathrm{kg}{\mathrm{m}}^{-1}$

Let I be the current flowing.

For equilibrium,

$mg\mathrm{sin}30\xb0=IlB\mathrm{cos}30\xb0$

$I=\frac{mg}{lB}\mathrm{tan}30\xb0=\frac{0.5\times 9.8}{0.25\times \sqrt{3}}=11.32\mathrm{A}$

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