Question

A small metallic sphere is hung by an insulating thread between two plates $A$ and $B$ with uniform distribution of point charges on their surface. A neutral sphere is hung at the mid point between plates. The net force on the sphere is:

• A. zero
• B. towards plate $A$
• C. towards plate $B$
• D. vertically upwards

Answer 1

The correct option is A zero


The sphere will get $-ve$ charge on the half surface and $+ve$ charge on the other half surface, due to induction from plates.
The net attractive force experienced by first half part of sphere will get cancelled out with net attractive force experienced by the second half part.
$\therefore F_{\text{net}}=0$
The answer is independent of the position of the sphere between the plates.

$\begin{array}{c}\text{Why this question ?}\\ \text{Bottomline: The charge on plate can be considered as}\\ \text{combination of large number of point charges.}\\ \text{Thus for each point on sphere, equal and opposite}\text{attractive forces are exerted by both plates.}\end{array}$