In 1942, Boris Podolsky proposed a generalization of electrostatics that eliminates the divergence of the Coulomb field

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In 1942, Boris Podolsky proposed a generalization of electrostatics that eliminates the divergence of the Coulomb field for a point charge. His theory retains ∇ ×E = 0 but replaces Gauss’ law by

(a) Find the electric field predicted by this equation for a point charge at the origin by writing E = −∇ϕ and integrating the equation over an infinitesimal spherical volume. It will be convenient at some point to write

(b) Suggest a physical meaning for the parameter a.

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