## First analytic correction beyond the proximity force approximation in the Casimir effect for the electromagnetic field in sphere-plane geometry

We consider the vacuum energy for a configuration of a sphere in front of a plane, both obeying the conductor boundary condition, at small separation. For the separation becoming small we derive the first next-to-leading order of the asymptotic expansion in the separation-to-radius ratio {epsilon}. This correction is of order {epsilon}. Opposite to the scalar cases it contains also contributions proportional to logarithms in first and second order, {epsilon}ln{epsilon} and {epsilon}(ln{epsilon}){sup 2}. We compare this result with the available findings of numerical and experimental approaches.