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  4. A metallic rod of mass unit length 0.5 kg m -1 is lying horizontally on a smooth inclined plane which makes an angle of 30° with the horizontal. A magnetic field of strength 0.25 T is acting on it in the vertical direction. When a current ' T ' is flowing through it, the rod is not allowed to slide down. The quantity of current required to keep the rod stationary is

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Q. A metallic rod of mass unit length $0.5 \,kg\, m ^{-1}$ is lying horizontally on a smooth inclined plane which makes an angle of $30^{\circ}$ with the horizontal. A magnetic field of strength $0.25\, T$ is acting on it in the vertical direction. When a current ' $T$ ' is flowing through it, the rod is not allowed to slide down. The quantity of current required to keep the rod stationary is

KCETKCET 2022Moving Charges and Magnetism

Solution:

$F = Bil$
$Bil \cos \theta= mg \sin \theta$
$0.25 \times I \times \frac{\sqrt{3}}{2}=0.5 \times 10 \times \frac{1}{2}$
$I =\frac{5 \times 100}{25 \times \sqrt{3}}=\frac{20}{\sqrt{3}} A$
$I =11.32 \,A$