Question

Four particle 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. $\frac{q}{4\pi {ϵ}_0{a}^2}$ Along OE
• B. $\frac{q}{3\pi {ϵ}_0{a}^2}$ Along OE
• C. $Zero$
• D. $\frac{q}{5\pi {ϵ}_0{a}^2}$ Along EO

Answer 1

The correct option is D $\frac{q}{5\pi {ϵ}_0{a}^2}$ Along EO

Charge $=q$

distance of each corner from the centre $=a$

If there is a charge at $5th$ vertex of polygon.

$F_1+F_2+F_3+F_4+F_5=0⟶\left(1\right)$

From the above equation there is no charge at $5th$ vertex so $F_5$ should be eliminated from equation $\left(1\right)$

$F_1+F_2+F_3+F_4+F_5=F_5$

Net force at the center is $-Ve$

$F_5=\frac{1}{5}\frac{q}{\pi {ϵ}_0{a}^2}$ along $EO$