JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Magnetic Effects of Current

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 ______.

Answer: 9

Solution

The field is directed along the 13 cm hypotenuse, so the force on the 5 cm side is

F = I L B sin θ

, where

θ

is the angle between that side and the hypotenuse. In the 5-12-13 triangle this angle has

sin θ = \frac{12}{13}

. Thus

F = 2 \times (5 \times 1 0^{- 2}) \times 0.75 \times \frac{12}{13} = \frac{9}{130}

N. Comparing with

\frac{x}{130}

N gives

x = 9

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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