question_answer

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 [AIEEE 2005]

A) 2L

B) L/4  

C) 8L 

D) 4L

Correct Answer: A

Solution :

[a] Suppose that a point B, where net electric field is zero due to charges 8 q and

The electric field at B due charge 8 q at O,

and the electric field at B due to charge -2q at A,

According to condition,

\[\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{8q}{{{a}^{2}}}\,=\frac{1}{4\pi {{\varepsilon }_{0}}}\,\frac{2q}{{{(a+L)}^{2}}}\]

Thus, at distance 2L from origin, net electric field will be zero.