Question

Three point charges each of value +q are placed on three vertices of a square of side a metre,What is the magnitude of the force on a point charge of value -q coulomb placed at the centre of the square?

• A. $\frac{1}{4\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$
• B. $\frac{1}{2\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$
• C. $\frac{1}{\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$
• D. $\frac{2}{\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$

Answer 1

The correct option is B $\frac{1}{2\pi {\epsilon }_0}{\left(\frac{q}{a}\right)}^2$

Force due to charge on corner A= $\frac{1}{4\pi ϵ}\frac{q^2}{(a/\sqrt{2}{)}^2}\overrightarrow{OA}$

Force due to charge on corner B= $\frac{1}{4\pi ϵ}\frac{q^2}{(a/\sqrt{2}{)}^2}\overrightarrow{OB}$

Force due to charge on corner C= $\frac{1}{4\pi ϵ}\frac{q^2}{(a/\sqrt{2}{)}^2}\overrightarrow{OC}$

Total Force = $\frac{1}{4\pi ϵ}\frac{q^2}{(a/\sqrt{2}{)}^2}=\frac{1}{2\pi ϵ}\frac{q^2}{(a{)}^2}\overrightarrow{OC}$