Question

Four particles, each having a charge q are placed on the four corners A,B,C,D of a regular pentagon ABCDE. The distance of each corner from the centre is a. Find the electric field at the centre of the pentagon.

Answer 1

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Answer 2

Given :

A pentagon with four particles at its corners .

Distance of each corner from the center of the pentagon = a

To find :

The electric field at the center .

Solution :

Let suppose at the corner E , we place a particle with charge q .

Then , by symmetry , the net field at the center O will be zero .

That means the combined electric field by all four corners are equal and opposite of the electric field of charge at corner E .

Thus , the elctric field at center O due to corners A , B , C and D is ( q / 4π∈0 ) * $a^{2}$ along OE .  

The electric field at the center is ( q / 4π∈0 ) * $a^{2}$ along OE .