Question

A disc has charge distribution sigma and radius R . What is the Electric Field in N/C at a point P , located a distance x directly above the center of the disc?Write your answer in terms of sigma, R ,x , k, and pi (type "pi"). Indicate multiplication with a "*" and division with a "/".

Answer 1

The charge between radii r and r + dr on the disk is:

sigma 2 pi r dr

The contribution to the potential from this charge is:

sigma/(4 pi epsilon) 2 pi r dr/sqrt(r^2 + x^2)

Integrating over r from 0 to R gives:

V(x) = sigma/(2 epsilon) [sqrt(R^2 + x^2) - x]

By symmetry, the electric field only has a component in the x-direction, this is minus the derivative of the potential w.r.t. x:

E(x) = sigma/(2 epsilon) [1 - x/sqrt(R^2 + x^2)]