# Gauss's Law and Finding the electric field

1.
Two long charged, concentric cylinders have radii of 3.0 and 6.0 cm. The charge per unit length is 5.0 x 10-6 C/m on the inner cylinder and -7.0 x 10-6 on the outer cylinder. Find the electric field at (a) r = 3.0 cm and (b) r = 8.0 cm, where r is the radial distance from the common central axis.

ε0 ∮EdA = qenc
λ= Q/L

## The Attempt at a Solution

EA = qenc0

E = λL/ π r2 ε0

From here, I don't know what to do with L. The height of the cylinder should be irrelevant, right?
I have another similar question using ρ and volume, leaving me with a height in the formula for the volume that I don't know what to do with.

Thanks.

ehild
Homework Helper
EA = qenc/ε0

this is the right formula, just make it clear, what A is.

ehild

I figured out what I was doing wrong. The area is the surface area of the cylinder, not the area of the base. So, L cancels when (2 pi r)h is in the denominator.

ehild
Homework Helper
I figured out what I was doing wrong. The area is the surface area of the cylinder, not the area of the base. So, L cancels when (2 pi r)h is in the denominator.

Well done!

ehild