Question

A small charged ball is hovering in the state of equilibrium at a height h over a large horizontal uniformly charged sheet. What would be the acceleration of the ball if a disc of radius
r = 0.001h is removed from the plate directly underneath the ball-

• A. $\frac{g}{2}\left( \frac{r}{h} \right)^{2}$
• B. $\frac{g}{2}\left( \frac{h}{r} \right)^{2}$
• C. $\frac{g}{4}\left( \frac{r}{h} \right)^{2}$
• D. $\frac{g}{4}\left( \frac{h}{r} \right)^{2}$

Answer 1

Answer: (A)

$\frac{g}{2}\left( \frac{r}{h} \right)^{2}$

Answer 2

Equilibrium mg = qE

Now s × pr² charged disc is removed.

As r is very less we can treat disc as a point charge

unbalanced acceleration = ×

Q = s × pr² ; q = $\frac { \mathrm { mg } } { \mathrm { E } }$

putting in acceleration expression

a = $\frac { g } { 2 } \left( \frac { r } { h } \right) ^ { 2 }$