Question

A metal disc of radius $a$ rotates with a constant angular velocity $\omega$ about its axis. The potential difference between the center and the rim of the disc is ($m=$ mass of electron, $e=$ charge on electron)

• A. $\frac{m{\omega }^2{a}^2}{e}$
• B. $\frac{1}{2}\frac{m{\omega }^2{a}^2}{e}$
• C. $\frac{e{\omega }^2{a}^2}{2m}$
• D. $\frac{e{\omega }^2{a}^2}{m}$

Answer 1

The correct option is B $\frac{1}{2}\frac{m{\omega }^2{a}^2}{e}$

For second law of Motion,

$F=ma$

$eE=m{w}^{2}r$

$E=\frac{m{w}^{2}r}{e}$

The potential difference $V=\int E.dr$

$V=\frac{{\int }_0^{a}m{w}^{2}r}{e}=\frac{m{w}^2{a}^2}{2e}$