(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A metallic spherical shell of radiusis cut in half at its equator. The two halves are separated very slightly and are maintained at potentials [itex]+V_{0}[/itex] and [itex]-V_{0}[/itex]. I am trying to find the electric field at the center of the sphere.a

2. Relevant equations

The equation for the potential of the sphere was calculated using Laplace's equation in spherical polar coordinates using separation of variables, and was found to be as follows:

[itex]V(r,\vartheta)[/itex]=[itex]\sum[/itex]A[itex]_{2m+1}[/itex]r[itex]^{2m+1}[/itex][itex]P_{2m+1}(Cosθ[/itex])

where "P" represents Legendre polynomials.

3. The attempt at a solution

Trivially I think it should be zero and taking the gradient of the above equation seems to support this for r=0, θ=Pi/2; however, I am unsure if this is correct reasoning. Any assistance would be greatly appreciated, thanks!

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# Electric Field of a Spherical Shell Cut in Half

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