Question

$n$ charges $Q,4Q,9Q$, ..... are placed at distances of $1m,2m,3m$ ..... respectively from a point on the same straight line. The electric intensity at that point is :

• A. $\frac{Q}{4\pi {ϵ}_0{n}^2}$
• B. $\frac{Q}{4\pi {ϵ}_{0}n}$
• C. Infinity
• D. $\frac{nQ}{4\pi {ϵ}_0}$

Answer 1

Answer: (D)

$\frac{nQ}{4\pi {ϵ}_0}$

Since all charges have same sign and lie on a same straight line, so for calculating electric field intensity we can add them directly i.e,

$\Rightarrow E=\frac{k\left(Q\right)}{1^2}+\frac{k\left(4Q\right)}{2^2}+\frac{k\left(9Q\right)}{3^2}+\frac{k\left(16Q\right)}{4^2}+.....$
$E=KQ+KQ+KQ+KQ+......$
$E=nKQ$ (since there are 'n' charges)

$E=\frac{nQ}{4\pi {ϵ}_0}$