Part A: A very long solid cylinder of radius R has a positive charge uniformly distributed throughout it, with charge per unit volume ρ. From the expression for E for this cylinder: E(r)=λr/2πϵ0R^2 for r≤R and E(r)=λ/2πϵ0r for r≥R, find the expressions for the electric potential V as a function of r, both inside and outside the cylinder. Let V= 0 at the surface of the cylinder. In each case, express your result in terms of the charge per unit length λ of the charge distribution. Express your answer in terms of the given quantities and appropriate constants. V(r)(r>R)=? Part B Express your answer in terms of the given quantities and appropriate constants. V(r)(r<R)=?
Part A: A very long solid cylinder of radius R has a positive charge uniformly distributed throughout it, with charge per unit volume ρ. From the expression for E for this cylinder: E(r)=λr/2πϵ0R^2 for r≤R and E(r)=λ/2πϵ0r for r≥R, find the expressions for the electric potential V as a function of r, both inside and outside the cylinder. Let V= 0 at the surface of the cylinder. In each case, express your result in terms of the charge per unit length λ of the charge distribution.
Express your answer in terms of the given quantities and appropriate constants. V(r)(r>R)=?
Part B
Express your answer in terms of the given quantities and appropriate constants. V(r)(r<R)=?
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