A single turn current loop in the shape of a right angle triangle… | JEE Main 2023 (24 Jan, Shift 2)

Q31JEE Main 2023 · 24 JAN · SHIFT 2Medium

Force on Current-Carrying Conductors

A single turn current loop in the shape of a right angle triangle with sides 5 cm, 12 cm, 13 cm is carrying a current of 2 A. The loop is in a uniform magnetic field of magnitude 0.75 T whose direction is parallel to the current in the 13 cm side of the loop. The magnitude of the magnetic force on the 5 cm side will be $\frac{x}{130}$ N. The value of $x$ is ____________.

Numerical answer type. Work it out, then open the answer.

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Answer: 9

$B$ is along the 13 cm side; angle $\theta$ between the 5 cm side and the hypotenuse has $\sin\theta = \frac{12}{13}$ .
$F = I L B \sin\theta = 2\times0.05\times0.75\times\frac{12}{13}$
$F = \frac{0.9}{13} = \frac{9}{130}\text{ N}$
$x = 9$

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