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

Explanation

If there had been a sixth charge +q at the remaining vertex of hexagon due to all the six charges on -q at O will be zero (as the forces due to individual charges will balance each other).

Now if `vec(f)` is the force due to sixth charge and `vec(F)` due to remaining five charges.
`vec(F)+vec(f)=0 rArr vec(F)=-vec(f) rArr F=f=(1)/(4pi epsilon_(0))(qxxq)/(L^(2))=q^(2)/(4pi epsilon_(0)L^(2))`