Question

Five point charges each of value +q are placed on five vertices of a regular hexagon of side ? `a' m. What is the magnitude of force on a point charge of s slue '-q' coulomb placed at the centre of hexagon ?

• A. $\frac{1}{4\pi {ϵ}_0}\frac{q^2}{a^2}$
• B. $\frac{1}{4\pi {ϵ}_0}\frac{q^2}{5a^2}$
• C. $\frac{1}{4\pi {ϵ}_0}\frac{{5q}^2}{a^2}$
• D. $\frac{1}{4\pi {ϵ}_0}\frac{{3q}^2}{a^2}$

Answer 1

The correct option is A $\frac{1}{4\pi {ϵ}_0}\frac{q^2}{a^2}$

If there were 6 charges at each corner then the net electric field at the centre would be zero since it is a regular hexagon . the electric field due to 5 charges will be equal and opposite to the net electric field due to sixth charge so as to make the net electric field at the centre to be zero . Hence electric field at the centre due to 5 charges is will be equal to electric field at the centre due to sixth charge

F = K q²/a² where K is 1/4π€