Question

four particles 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 then find the electric field at the centre of the Pentagon​

Answer 1

If there were 5 charges at each corner then the net electric field at the centre would be 0 since it is a regular polygon .

the electric field due to 4 charges will be equal and opposite to the electric field due to the 5th charge so as to make the net electric field at the centre to be 0

Hence electric field at the centre due to 4 charges = electric field at the centre due to the 5th charge

=

$q \div 4\pi \times e0 \times {a}^{2}$