Question

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

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

Answer 1

Answer: (A)

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

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 =$\frac{Q}{4\pi\varepsilon_{0}h^{2}}$×$\frac{q}{m}$

Q = s × pr²

q = $\frac{mg}{E}$

Putting in acceleration expression

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