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. $\frac{\operatorname{m} \omega^{2} x }{ e }$
• B. $\frac{m \omega x}{e l}$
• C. $\frac{m x}{\omega^{2} l}$
• D. $\frac{m e}{\omega^{2} x}$

Answer 1

Answer: (A)

$\frac{\operatorname{m} \omega^{2} x }{ e }$

Answer 2

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