Question

A charge ${+10}^{-9}C$ is located at the origin in free space and another charge $Q$ at $(2,0,0)$. If the $X-$component of the electric field at $(3,1,1)$ is zero, calculate the value of $Q$. Is $Y-$component zero at $(3,1,1)$?

Answer 1

As electric field along x axis is zero at (3,1,1), we can say that the electric field due to charge Q is equal in magnitude and opposite in direction to the field due to charge ${10}^{-9}$ C.

Thus value of charge Q can be obtained as

$\frac{Q}{3^2}=\frac{{10}^{-9}}{2^2}\Rightarrow Q=20.25\times {10}^{-9}\text{C}$

The field along Y axis is due to charge Q only and is given by

$\frac{20.25\times {10}^{-9}}{4\pi {ϵ}_0\left(1^2\right)}$ = 182.25 units