Question

A copper rod AB of length $l$ is rotated about end A with a constant angular velocity $\omega$. Find electric field at a distance $x$ from the axis of rotation :

• A. $\frac{m{\omega }^{2}x}{e}$
• B. $\frac{m\omega x}{el}$
• C. $\frac{mx}{{\omega }^{2}l}$
• D. $\frac{me}{{\omega }^{2}x}$

Answer 1

The correct option is A $\frac{m{\omega }^{2}x}{e}$

We know in circular motion net force acting on it must be $\frac{m{v}^2}{r}$

When rod rotates , electrons in it also rotates which produce electric field $E$ at distance $x$ .
force on the electron $F_e=eE=m{\omega }^{2}x$

Therefore,
$\Rightarrow Ee=\frac{m{v}^2}{x}$(we know $v=xw$)
$\Rightarrow Ee=\frac{m(xw{)}^2}{x}$
$\Rightarrow E=\frac{m{w}^{2}x}{e}$