oblem 23.67 - Copy Part A A very long solid cylinder of radius R has positive ch

Question

oblem 23.67 - Copy Part A A very long solid cylinder of radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. From the expression for E for this cylinder: E(r)=?r2??0R2 for r?R and E(r)=?2??0r 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 ? of the charge distribution. Express your answer in terms of the given quantities and appropriate constants.

Part A V(r)(r>R) = Part B Express your answer in terms of the given quantities and appropriate constants.
oblem 23.67 - Copy oblem 23.67 - Copy Part A A very long solid cylinder of radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. From the expression for E for this cylinder: E(r)=?r2??0R2 for r?R and E(r)=?2??0r 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 ? of the charge distribution. Express your answer in terms of the given quantities and appropriate constants.

Part A V(r)(r>R) = Part B Express your answer in terms of the given quantities and appropriate constants.
Part A A very long solid cylinder of radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. From the expression for E for this cylinder: E(r)=?r2??0R2 for r?R and E(r)=?2??0r 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 ? of the charge distribution. Express your answer in terms of the given quantities and appropriate constants.

Part A V(r)(r>R) = Part B Express your answer in terms of the given quantities and appropriate constants.
Part A A very long solid cylinder of radius R has positive charge uniformly distributed throughout it, with charge per unit volume ?. From the expression for E for this cylinder: E(r)=?r2??0R2 for r?R and E(r)=?2??0r 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 ? of the charge distribution. Express your answer in terms of the given quantities and appropriate constants.

Part A V(r)(r>R) = Part B Express your answer in terms of the given quantities and appropriate constants.
Part B Express your answer in terms of the given quantities and appropriate constants.

Explanation / Answer

a)

r>R:

V = int{-lamda/(2pie0r) dr} =-lamda/(2 pi e0) Ln(r/R) = lamda/(2 pi e0) Ln(R/r)

b)

V = int{-(lamda r)/(2pie0R^2) dr} =-lamda/(2 pi e0 R^2) (r^2/2 - R^2/2) = lamda/(4 pi e0 R^2) (R^2 - r^2)

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