Question

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the x-axis at which the net electric field due to these two point charges is zero is :

• A. $2L$
• B. $\frac{L}{4}$
• C. $8L$
• D. $4L$

Answer 1

Answer: (A)

Suppose that a point $B$ , where net electric field is zero due to charges $8q$ and-$2q.$
${\overrightarrow{E}}_{BO}$$=\frac{-1}{4\pi {\epsilon }_0}.\frac{8q}{a^2}\hat{i}$
${\overrightarrow{E}}_{BA}$$=\frac{1}{4\pi {\epsilon }_0}.\frac{+2q}{{\left(a+L\right)}^2}\hat{i}$
According to condition ${\overrightarrow{E}}_{BO}$ +${\overrightarrow{E}}_{BA}=0$
$\therefore \frac{-1}{4\pi {\epsilon }_0}.\frac{8q}{a^2}=\frac{1}{4\pi {\epsilon }_0}\frac{2q}{{\left(a+L\right)}^2}$
$\Rightarrow \frac{2}{a}=\frac{1}{a+L}$
$\Rightarrow 2a+2L=a$
$\therefore 2L=-a$
Thus, at distance $2L$ from oxigin, net electric field will be zero.