Question

Two electric charges $2q$ and $8q$ are placed at a distance of $6a$ on a horizontal plane. The distance of the location of the point from charge $2q$ where the electric field is zero is

• A. $2a$
• B. $a$
• C. $1.5a$
• D. $2.5a$

Answer 1

The correct option is A $2a$

Given 2 charges $2q$ & $8q$ are pleased at a distance of $6a$ on a horizontal plan.

suppose $+ve$ charge $+2q$ is placed at origin and charge $+8q$ is placed at (6a,0).

Let point p on the$x$-axis at the distance $"x"$ from the origin when the electric field is zero.

Electric field at P due to Chang 2q

$E_1=k.\frac{2q}{x^2}$

Electric field at P due to Chang 8q

$E_2=k.\frac{8q}{{(6a-x)}^2}$

the net electric to be zero

means $E_1=E_2$

ie,

$k.\frac{2q}{x^2}=k.\frac{8q}{{(6a-x)}^2}\Rightarrow {(6a-x)}^2=4x^2$

Taking square root on both sides

$6a-x=2x6a=3xx=2aso,$

the answer is option (a).