Answer: Magnitude of electric field =p × Ke × Q/d^3
Explanation: Using Coulombs law of point charge,each charge on the circle would exert a fieldEc at point given by:
Ec= Ke × (Q/n)/d^2
Where Ke= Coulomb's constant
d= distance between the charges and the point of measurement, P with d^2=a^2+p^2
(Q/n)= Magnitude of the charge.
For charges in a circle,all the force components and direction(x,z) are cancelled by the symmetry,leaving only the vertical force(y-direction)
The Resultant vector will be
Ecy=Eq × sin(theta)
Ecy=Ke × (Q/n)/d^2 ×(p/d)
Adding the forces from all the charges,the magnitude of electric field Ey=n×Ecy
/Ey/= n ×[Ke ×(Q/n)/d^2 ×(p/d)]
/Ey/= p × Ke × (Q/d^3)