Question

A hypothetical magnetic field existing in a region is given by $\underset{B}{\to }=B_0\underset{e_r}{\to }$ where $\underset{e_r}{\to }$ denotes the unit vector along the radial direction. A circular loop of radius a, carrying a current i, is placed with its plane parallel to the x - y plane and the centre at (0, 0, d). Find the magnitude of the magnetic force acting on the loop.

Answer 1

Required magnetic force

$F=\int dF={\int }_0^{2\pi a}idlBsin\theta =iB.\frac{a}{\sqrt{a^2+d^2}}{\int }_0^{2\pi a}dl=\frac{2\pi a^{2}B}{\sqrt{a^2+d^2}}$