The magnetic field existing in a region is given by \(\overrightarrow{\mathrm{B}}=0.2(1+2 \mathrm{x}) \hat{\mathrm{k}} \mathrm{T}\). A square loop of edge 50 cm carrying 0.5 A current is placed in \(\mathrm{x}-\mathrm{y}\) 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 .

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Magnetic Effects of Current

The magnetic field existing in a region is given by

B = 0.2 (1 + 2 x) \hat{k} T

. 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 .

Answer: 50

The field

B = 0.2 (1 + 2 x) \hat{k}

varies only with

x

. The two loop sides parallel to the

x

-axis experience forces that cancel, so the net force comes from the two sides parallel to the

y

-axis (length

ℓ = 0.5

m), sitting at

x_{1}

and

x_{2} = x_{1} + 0.5

F_{net} = I ℓ [B (x_{2}) - B (x_{1})] = I ℓ (0.2) (2) (x_{2} - x_{1}) .

This depends only on the edge length

Δ x = 0.5

m, not on the loop's absolute position:

F_{net} = 0.5 \times 0.5 \times 0.4 \times 0.5 = 0.05 N = 50 mN .

Answer: 50.

JEE Main · 2024 · 04 Apr 2024 · Shift 1 · Integer answer