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.

Explanation

Let the forces `F_1,F_2,F_3,F_4` and `F_5` acting due to the charges`Q_1,Q_2,Q_3,Q_4` and `Q_5` respectively.

From the `F_1 = F_5` and act in opposite directions. Hence they cancel each other.
`F_2 sin45^@ = F_4sin45^@`
They are also equal and opposite. So they cancel each other.
Electrostatic force
`F_("tot") = F_3+F_2cos45^@+F_4cos45^@`
`F_("tot") = (KqQ)/R^2+(KqQ)/R^2xx1/sqrt(2)+(KqQ)/R^2 xx 1/sqrt(2)`
`= {(KqQ)/R^2+2(KqQ)/R^2xx1/sqrt(2)}hati`
`F_("tot")= {(KqQ)/R^2+sqrt(2)(KqQ)/R^2}hati`
`= 1/(4piepsilon_0)(qQ)/R^2[1+sqrt(2)]hatiN ` `[K = 1/(4piepsilon_0)]`
`:.` Electrostatic force experienced by the charge q is `F_("tot") = 1/(4piepsilon_0)(qQ)/R^2[1+sqrt(2)]hatiN`