Answer to Question #290081 in Electric Circuits for Job

Question

A wire is Bent into a circle of radius a and a total charge Q is distributed uniformly around it.find the magnetic field at the center if the wire rotates with an angular velocity w about the axis of the circle

Answer 1

Given charge q, rotating in a circular motion of radius a

Linear charge density, $\lambda=\frac{q}{2 \pi a}$

Time period, $T= \frac{2 \pi}{w}$

Current in circular motion, $I=\frac{q}{T}=\frac{qw}{2 \pi}$

Magntic field, $B= \frac{\mu_oqw}{2a}=\frac{\mu_oqw}{2a}×\frac{ q}{2 \pi a}=\frac{\mu_oqw}{4\pi a}$

Magnetic field at the centre is $\frac{\mu_oqw}{4\pi a}$