Question

Figure shows a square loop. $20\text{cm}$ on each side in the x-y plane with its centre at the origin. The loop carries a current of $7\text{A}$.
Above it at $y=0,z=12\text{cm}$ is an infinitely long wire parallel to the x-axis carrying a current of $10\text{A}$. The net force on the loop is ———$\times {10}^{–5}\text{N}$.

Answer 1

When viewed along $x$ axis, force on $BC\&DA$ of loop can be considered as



Force due to infinite long wire on $AB\&CD$ cancel eachother
Net force $F=(F_1+F_2)\sin \theta$
We know that $F_1=F_2=\left[\frac{{\mu }_0{i}_1{i}_2}{2\pi r}\right]\left[a\right]$
$F=\left[\frac{{\mu }_0{i}_1{i}_{2}2a}{2\pi r}\right]\left[\frac{a}{2r}\right]$
$F=\left[\frac{{\mu }_0{i}_1{i}_2{a}^2}{2\pi r^2}\right]$
$F=\frac{2\times {10}^{-7}\times 7\times 10\times 400\times {10}^{-4}}{244\times {10}^{-4}}$
$F=0.23\times {10}^{-4}$
$F=2.3\times {10}^{-5}\text{N}$