Consider a wireframe shown in figure. Equal currents $I$ flow through all the three branches of the wire frame. The frame is a combination of two semicircles $A C D$ and $C D E$ of radius $a$ . It is placed in uniform magnetic field B acting perpendicular to the plane of frame. The magnitude of magnetic force acting on the frame is

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$6 B I a$

$3 B I A$

$B I a$

Zero

answer is A.

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Detailed Solution

${\vec{F}}_{C A D} = {\vec{F}}_{C D} = {\vec{F}}_{C E D} = B I l_{e f f} = B I (2 a)$
Net force on the frame is $\vec{F} = 3 {\vec{F}}_{C D}$
$\Rightarrow | \vec{F} | = 6 B I a {F = I l B}$

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