Question

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

• 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

Answer: (A)

We know in circular motion net force acting on it must be $\frac{m{v}^2}{r}$
When the rod rotates, electrons in it also rotates which produce electric field $E$ at distance $x$.
Force on the electron, $Fe=eE=m{\omega }^{2}x$
$\therefore Ee=\frac{m{v}^2}{x}(v=x\omega )$
$Ee=\frac{m(x\omega {)}^2}{x}$
$\Rightarrow E=\frac{m{\omega }^{2}x}{e}$