# Gauss' Law With an Infinite Cylinder of Charge

[SOLVED] Gauss' Law With an Infinite Cylinder of Charge

## Homework Statement

The test question was to find the potential difference between a point S above a cylinder of charger per length lambda, and a point on the surface of the cylinder having radius R and infinite length.

## Homework Equations

Stupid me tried to grind through it during the test. But looking at the prof's solution:

http://www.phys.washington.edu/users/schick/321A/321-07exam1soln.pdf

Here's the test if you need to know the question how he worded it:

http://www.phys.washington.edu/users/schick/321A/321-07exam1.pdf

Problem #1.

I don't get how he got "E(s)*2pi*L*S

I get the 2pi and L come from integrating over phi and the length of the cylinder, but I can't figure out where that S came from.

Is it because you'd need a cosine(theta) for the direction that the cylinder is from S? Where cosine is S/distance? Then wouldn't he have to add in a bunch of other stuff? I'm just not seeing something here and I feel embarrassed.

$$\int E \cdot dA = EAcos(\Theta)$$
Where $$\Theta$$ is the angle between the surface of the cylinder and the electric field.
Now, simplify this last expression. What is A? What is $$\Theta$$?