Question

Charges q-q and q coulomb are placed at the points $(-\hat{i}+\hat{j}+\hat{k}),(-\hat{i}-\hat{j}+\hat{k})$ and $(-\hat{i}+\hat{j}-\hat{k})$ respectively. The x-component of electric field at the origin will be

• A. $\frac{1}{4\pi {\epsilon }_0}.\frac{q}{3\sqrt{3}}$
• B. $\frac{1}{4\pi {\epsilon }_0}.\frac{2q}{3\sqrt{3}}$
• C. $\frac{1}{4\pi {\epsilon }_0}.\frac{q}{\sqrt{3}}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{4\pi {\epsilon }_0}.\frac{q}{3\sqrt{3}}$

Charges $q-q$

$q$ coulomb points $(-i+j+k)$, $(-i-j+k)$, $(-i+j-k)$ respectively,

charges will be taken $=\frac{q}{3}$

Now, $E=1$

$d=\sqrt{1^2+1^2+1^2}=\sqrt{3}$ unit

$E=\frac{1}{4\pi {ϵ}_0}\frac{q}{3\sqrt{3}}$