Suppose the electrostatic potential of a point charge were (r) = (1/4 0 )r (1+) rather than

Suppose the electrostatic potential of a point charge were ϕ(r) = (1/4πε₀)r ^−(1+ε) rather than the usual Coulomb formula.

(a) Find the potential ϕ(r) at a point at a distance r from the center of a spherical shell of radius R > r with uniform surface charge per unit area σ. Check the Coulomb limit ε = 0.

(b) To first order in ε, show that

Since the time of Cavendish, formulae like this one have been used in experimental tests of the correctness of Coulomb’s law.

Transcribed Image Text:

y(R) — 9(r) 9(R) 2 R [A R+r r R-r In - In 4R² =]. R² r²