The electric field along the axis of a uniformly charged disk of radius R and total charge Q is given below.
Ex = 2πkeσ(1 − x/(x2 + R2)^1/2)
Show that the electric field at distances x that are large compared with R approaches that of a particle with charge
Q = σπR^2.
Suggestion: First show that
x/(x2 + R2)^1/2 = (1 + R2/x2)^−1/2,
and use the binomial expansion
(1 + δ)n ≈ 1 + nδ
δ « 1.