If the photon had a mass m, Gauss law with E = changes from 2

If the photon had a mass m, Gauss’ law with E = −∇ϕ changes from ∇²ϕ = −ρ/ ε₀ to an equation which includes a lenght L = − ђ/mc:

Experimental searches for m use a geometry first employed by Cavendish where a solid conducting sphere and a concentric, conducting, spherical shell (radii r₁ < r₂) are maintained at a common potential Ф by an infinitesimally thin connecting wire. When m = 0, all excess charge resides on the outside of the outer shell; no charge accumulates elsewhere.

(a) Use the substitution ϕ(r) = u(r)/r to solve the equation above in the space between the conductors. Find also the electric field in this region.

(b) Use the generalization of Gauss’ law for E implied by the foregoing equation for ϕ to find the charge Q of the conducting ball.

(c) Show that, to leading order when L→∞,

Transcribed Image Text:

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