Question

Consider n equal positively charged particles each of magnitude Q/n placed symmetrically around a circle of radius a. Calculate the magnitude of the electric field at a point a distance x from the center of the circle and on the line passing through the center and perpendicular to the plane of the circle. (Use any variable or symbol stated above along with the following as necessary: ke.)

Answer 1

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)