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- Homework Statement
- Electrodynamics: Conducting Sphere cut in half to form a gap, and a charge q is placed on the first half-sphere. Find all four σ, as well as E in the and the potential difference between the hemispheres.

- Homework Equations
- Anything Gauss' Law, boundary conditions, known features of a conductor, and any E-field derivations that come out of Coulomb's law.

Summary: Electrodynamics: Conducting Sphere cut in half to form a gap, and a charge q is placed on the first half-sphere. Find all four σ.

A sphere of radius R is cut in half to form a gap of s << R (ignore edge effects) - the first hemisphere is charged with q, and the second hemisphere is left uncharged.

My first question is to determine σ(r) on the plane face of the first hemisphere.

My personal question is as to whether or not this σ depends on r (ie non-constant). If it does, it is due to geometry. My question, then, is how does σ depend on r for the plane-face of the first half-sphere? Does the sphere being locally flat not constitute a constant σ of σ1(r)=1/3(Q/(3πR^2)) to account for 3S

The question later on asks for the electric field between the gap, so this answer should be obtainable before making that conclusion. I know that E must point straight from σ1 to σ2, as E must be normal to both of the surfaces since they are conductors.

A sphere of radius R is cut in half to form a gap of s << R (ignore edge effects) - the first hemisphere is charged with q, and the second hemisphere is left uncharged.

My first question is to determine σ(r) on the plane face of the first hemisphere.

My personal question is as to whether or not this σ depends on r (ie non-constant). If it does, it is due to geometry. My question, then, is how does σ depend on r for the plane-face of the first half-sphere? Does the sphere being locally flat not constitute a constant σ of σ1(r)=1/3(Q/(3πR^2)) to account for 3S

_{face}=S_{tot}The question later on asks for the electric field between the gap, so this answer should be obtainable before making that conclusion. I know that E must point straight from σ1 to σ2, as E must be normal to both of the surfaces since they are conductors.

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