A square loop of edge length $2\ \text{m}$ carrying a current of $2\ \text{A}$ is placed with its edges parallel to the $x$–$y$ axes. A magnetic field is passing through the $x$–$y$ plane and expressed as $\vec B = B_0(1 + 4x)\hat k$, where $B_0 = 5\ \text{T}$. The net magnetic force experienced by the loop is ______ N.
Numerical value type. Enter your answer.
Answer: 160
The forces on the two edges parallel to the $x$-axis cancel (at each $x$ the field is the same for both, and the currents are opposite).
The two edges parallel to the $y$-axis are at $x_1$ and $x_1 + 2$ and carry opposite currents, so the net force is
$$F = IL\left[B(x_1 + 2) - B(x_1)\right] = 2\times2\times B_0\times4\times2 = 2\times2\times5\times8 = 160\ \text{N}$$
Solution by Sreeraj P, M.Sc Physics