Question

Four particles. each having a charge q, are placed on the four vertices of a regular pentagon, The distance of each corner from the centre is a, Find the electric field at the centre of the pentagon :

• A. $0$
• B. $\frac{q}{4\pi {\epsilon }_0{a}^2}$
• C. $\frac{q}{2\pi {\epsilon }_0{a}^2}$
• D. $\frac{q}{8\pi {\epsilon }_0{a}^2}$

Answer 1

Answer: (B)

$\frac{q}{4\pi {\epsilon }_0{a}^2}$

charges are present on corners B,C,D,E.

total electric force will be along the direction $\overrightarrow{OA}$

magnitude of force = $2\frac{1}{4\pi {ϵ}_0}\frac{q}{a^2}cos{36}^{\circ }-2\frac{1}{4\pi {ϵ}_0}\frac{q}{a^2}cos{72}^{\circ }=\frac{1}{4\pi {ϵ}_0}\frac{q}{a^2}$