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 acceleration of the ball if a disc of radius r = 0.00lh is removed from the plate directly underneath the ball ?

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

Answer 1

Answer: (A)

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

Answer 2

Equilibrium mg = qE\

Now 6 × pr² charged disc is removed as r is very less we can treat disc as a point charge

\ unbalanced acceleration = $\frac{Q}{4\pi th^{2}}$ × $\frac{q}{m}$

Q = 6 × pr²

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

putting in acceleration expression

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