# Potential of charged cylinder

## Homework Statement

For the cylinder of uniform charge density in Fig. 2.26:
(a) show that the expression there given for the field inside the cylinder follows from Gauss’s law;
(b) find the potential φ as a function of r, both inside and outside the cylinder, taking φ = 0 at r = 0.

2. Homework Equations

## The Attempt at a Solution

I finished part a and got the correct answers. I’m a bit confused about b now. Particularly the bit at the end about taking the potential and radius at 0. Can anybody explain where I start here?

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kuruman
Homework Helper
Gold Member
Use Gauss Law to find the electric field in the two regions (or read them off the figure) and then just integrate from the axis of the cylinder out.

FS98
haruspex
Homework Helper
Gold Member
taking the potential and radius at 0.
Potential is always relative. There is, in principle, no absolute 0. In most electrostatics questions the convention is to set the potential to 0 at infinity, but in this case they are telling you to define the potential as zero at r=0. So the potential at infinity will not be zero.

FS98
then just integrate from the axis of the cylinder out.
Can you explain how and why this is done?

kuruman
$$V(r=B)-V(r=A)=-\int_A^B{\vec E \cdot d\vec r}$$
$$V(r)-0=-\int_A^r{\vec E \cdot d\vec r}$$