Question

A phonograph record of radius R, which carries a uniformly distributed charge Q, is rotating with constant angular speed $\omega$ figure. Find the magnetic field at the center of the disk.

• A. $\frac{{\mu }_{0}Q\omega }{R}$
• B. $\frac{{\mu }_{0}Q\omega }{\pi R^2}$
• C. $\frac{{\mu }_{0}Q\omega }{2\pi R}$
• D. $\frac{{\mu }_{0}Q\omega }{\pi R}$

Answer 1

The correct option is C

$\frac{{\mu }_{0}Q\omega }{2\pi R}$

Let a ring of radius x and of thickness dx

Then charge on that ring; $dq=\frac{2Qxdx}{R^2}$

Magnetic field at centre due to this ring; $dB=\frac{{\mu }_{0}i}{2x}$

$dB=\frac{{\mu }_{0}Q\omega }{2\pi R^2}dx$

Magnetic field due to whole disc $=\frac{\mu Q\omega }{2\pi R^2}{\int }_0^{R}dx=\frac{{\mu }_{0}Q\omega }{2\pi R}$