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The potential at the surface of a sphere (radius R) is given by V, = k sin?e where k is a constant. Assume there's no charge inside or outside the sphere. (a) Express the potential on the surface as a linear combination of Legendre polynomials Pa(cos6) = Ra(x), i.e, x = cose. (b) Find the potential V(r, e) inside and outside the sphere. (c) Find the surface charge density o(e) on the sphere.

The potential at the surface of a sphere (radius R) is given by V, = k sin?e where k is a constant. Assume there's no charge inside or outside the sphere. (a) Express the potential on the surface as a linear combination of Legendre polynomials Pa(cos6) = Ra(x), i.e, x = cose. (b) Find the potential V(r, e) inside and outside the sphere. (c) Find the surface charge density o(e) on the sphere.

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Please answer (a), (b), and (c).

The potential at the surface of a sphere (radius R) is given by V, = k sin?e where k is a constant. Assume there's no charge inside or outside the sphere. (a) Express the potential on the surface as a linear combination of Legendre polynomials Ra(cose) = Ra(x), Le, x= cos e. (b) Find the potential V(r, e) inside and outside the sphere. (c) Find the surface charge density o() on the sphere.
Transcribed Image Text:The potential at the surface of a sphere (radius R) is given by V, = k sin?e where k is a constant. Assume there's no charge inside or outside the sphere. (a) Express the potential on the surface as a linear combination of Legendre polynomials Ra(cose) = Ra(x), Le, x= cos e. (b) Find the potential V(r, e) inside and outside the sphere. (c) Find the surface charge density o() on the sphere.
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