Question

Five identical charges Q are placed equidistant on a semicircle as shown in the figure. Another point charge q is kept at the center of the circle of radius R. Calculate the electrostatic force experienced by the charge q.

Answer 1

Force acting on q due to Q₁ and Q₅ are opposite direction, so cancel to each other. Force acting on q due to Q₃ is 

Force acting on q due to Q₂ and Q₄

Resolving in two component method: 

(i) Vertical Component: Q₂ Sin θ and Q₄ Sinθ are equal and opposite direction, so they are cancel to each other.

(ii) Horizontal Component: Q₂ Sin θ and Q₄ cos θ are equal and same direction, so they can get added.

Resultant net force F