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Tough Physics Problem on electric field along uniformly charged disk?

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 = σπR2.

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.

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