The magnetic field existing in a region is given by B = 0.2(1 + 2x)k. A square loop of edge 50 cm carrying 0.5 A current is placed in x-y plane with its edges parallel to the x-y axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ mN. Numerical answer type. Work it out, then open the answer.

Answer: 50. Forces on the sides parallel to x cancel (same B variation along each). Fnet = I a [B(x+a) - B(x)] = I a×0.2×2a Fnet = 0.5×0.5×0.4×0.5 = 0.05 N Fnet = 50 mN

The magnetic field existing in a region is given by B = 0.2(1 + 2x)k… | JEE Main 2024 (4 Apr, Shift 1)

Q19JEE Main 2024 · 4 APR · SHIFT 1Medium

Force on Current-Carrying Conductors

The magnetic field existing in a region is given by $\vec{B} = 0.2(1 + 2x)\hat{k}$ . A square loop of edge $50\text{ cm}$ carrying 0.5 A current is placed in $x\text{-}y$ plane with its edges parallel to the $x\text{-}y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is _________ $\text{mN}$ .

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

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Answer: 50

Forces on the sides parallel to $x$ cancel (same $B$ variation along each).
$F_{net} = I a\,[B(x+a) - B(x)] = I a\times0.2\times2a$
$F_{net} = 0.5\times0.5\times0.4\times0.5 = 0.05\text{ N}$
$F_{net} = 50\text{ mN}$

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