Question

Three charges $q,–q$ and $q_0$ are placed as shown in the figure. The magnitude of the net force on the charge $q_0$ at point O is $[k=\frac{1}{\left(4\pi {\epsilon }_0\right)}]$

• A. $\frac{2kq{q}_0}{a^2}$
• B. $\frac{1}{\sqrt{2}}\frac{kq{q}_0}{a^2}$
• C. $\frac{\sqrt{2}kq{q}_0}{a^2}$
• D. $0$

Answer 1

The correct option is C $\frac{\sqrt{2}kq{q}_0}{a^2}$


$\overrightarrow{F_1}=\frac{kq{q}_0}{a^2}\hat{j}$

$\overrightarrow{F_2}=\frac{kq{q}_0}{a^2}(-\hat{i})$

$\therefore \overrightarrow{F}=\overrightarrow{F_1}+\overrightarrow{F_2}=\frac{kq{q}_0}{a^2}(-\hat{i}+\hat{j})$

$\therefore |\overrightarrow{F}|=\frac{kq{q}_0}{a^2}\left(\sqrt{2}\right)$