Question

Two point charges $+ 8\, q$ and $- 2\, q$ 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. $2\,L$
• B. $\frac{L}{4}$
• C. $8L$
• D. $4\,L$

Answer 1

The Correct Option is A

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