Question

$‘n^{\prime }$ charges $Q,-4Q,9Q,-16Q$...... are placed at distances of $1,2,3$ ..... metres from a point ‘O’ on the same straight line. Then field at ‘O’ is:

• A. Zero
• B. $\frac{Q}{4\pi {ϵ}_0}$
• C. Zero (or)$\frac{Q}{4\pi {ϵ}_0}$accordingly as $‘n^{\prime }$ is even (or) odd respectively.
• D. We cannot say.

Answer 1

The correct option is C Zero (or)$\frac{Q}{4\pi {ϵ}_0}$accordingly as $‘n^{\prime }$ is even (or) odd respectively.

$E$ due to all positive charge
$E=\frac{KQ}{1^2}+\frac{K\left(9Q\right)}{3^2}$
$E$ due to all negative charge
$E=\frac{-K\left(4Q\right)}{2^2}-\frac{K\left(16Q\right)}{4^2}$
$E$ due to all individual charge is $KQ$
If $n$ is even, all charges will get canceled out.
and if $n$ is odd, then all charges will not get canceled out.
$\therefore E=KQ$ ,when $n$ is odd
$E=\frac{Q}{4\pi {ϵ}_0}$; $n$ is odd
$E=0$ ; $n$ is even