Question

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

• A. $+2.4\times {10}^{-10}C$
• B. $-6.2\times {10}^{-20}C$
• C. $-4.3\times {10}^{-10}C$
• D. $-1.2\times {10}^{-20}C$

Answer 1

The correct option is C $-4.3\times {10}^{-10}C$

$\begin{array}{c}\overrightarrow{r_1}=3\hat{i}+\hat{j}+\hat{k}\\ r_1=\sqrt{3^2+1^2+1^2}=\sqrt{11}\\ r_2=\left(3-2\right)i+\hat{j}+\hat{k}\\ r_2=\sqrt{1+1+1}=\sqrt{3}m\end{array}$

Electric pick at P and Q

$\frac{{10}^{-5}}{4\pi {\in }_0{11}^{3/2}}\left(3i+\hat{j}+\hat{k}\right)+\frac{Q}{4\pi {\in }_0{3}^{3/2}}\left(i+\hat{j}+k\right)$

Now X component of field

$\begin{array}{c}\frac{{10}^{-9}}{4\pi {\in }_0{11}^{3/2}}+\frac{Q}{4\pi {\in }_0{3}^{3/2}}=0\\ Q=-4.27\times {10}^{-10}\end{array}$