First slide

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

A

7.14 A
B

5.98 A
C

14.76 A
D

11.32 A

Solution

Mass per unit length of a metallic rod
$\frac{m}{l} = 0.5 kg m^{- 1}$
Let I be the current flowing.
For equilibrium,
$m g \sin 30 ° = I l B \cos 30 °$
$I = \frac{m g}{l B} \tan 30 ° = \frac{0.5 \times 9.8}{0.25 \times \sqrt{3}} = 11.32 A$

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