A square loop of edge length $$2$$ m carrying current of $$2$$ A is placed with its edges parallel to the $$x$$-$$y$$ axis. A magnetic field is passing through the $$x - y$$ plane and expressed as $$\vec{B} = B_0(1 + 4x)\hat{k}$$, where $$B_0 = 5$$ T. The net magnetic force experienced by the loop is _______ N.

Let the square loop have its vertical sides located at positions $$x$$ and $$x + L$$, with side length $$L = 2\text{ m}$$.

$$F_{\text{net}} = F_{\text{right}} - F_{\text{left}}$$

$$\implies F_{\text{net}} = I L B_0 [1 + 4(x+L)] - I L B_0 [1 + 4x]$$ $$\implies F_{\text{net}} = 4 I B_0 L^2$$

$$\implies F_{\text{net}} = 4 \times 2 \times 5 \times (2)^2 = 160\text{ N}$$