The magnetic field existing in a region is given by $\vec B = 0.2(1 + 2x)\hat k\ \text{T}$. A square loop of edge $50\ \text{cm}$ carrying $0.5\ \text{A}$ current is placed in the $x$-$y$ plane with its edges parallel to the $x$-$y$ axes, as shown in the figure. The magnitude of the net magnetic force experienced by the loop is ______ mN.
Numerical value type. Enter your answer.
Answer: 50
The loop extends from $x = 2\ \text{m}$ to $x = 2.5\ \text{m}$. The forces on the two sides parallel to the $x$-axis cancel (same field pattern, opposite currents).
The sides parallel to the $y$-axis carry opposite currents in different fields:
$$B(2) = 0.2(1 + 4) = 1.0\ \text{T},\qquad B(2.5) = 0.2(1 + 5) = 1.2\ \text{T}$$
$$F = IL\big[B(2.5) - B(2)\big] = 0.5\times0.5\times0.2 = 0.05\ \text{N} = 50\ \text{mN}$$
Solution by Sreeraj P, M.Sc Physics