# Calculate the electric field strength inside and outside a wire

## Homework Statement

An infinitly long conducting cylinder of Radius R carries a unifom surface charge of (lambda per unit length) determine the electric field strength inside and outside the cylinder

## Homework Equations

integral (E.ds)= q/e0

## The Attempt at a Solution

im not really sure what to do at all i tried simply differentiating the equation above and substituting lambda in for q but im pretty sure thats not right...

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First, the field inside is easiest to start with. The q in integral (E.ds) = q/e0, is the charge inside a gaussian surface. So a gaussian surface inside the conductor encloses how much charge? ... so the electric field is...?

Next, you need to simply integrate the left side of the equation after subtituting dr for ds. Then use a gaussian surface of some length l, and figure out what the q enclosed is and plug that into the right side.

so since its a Gaussian surface do i calculate the line charge density by integrating lambda from R to infinity? then substitute that into the equation above?

Electric field inside the cylinder is zero. Because that is conductor material

ok so outside the conductor do i just use the E=q/4(pi)e0R^2 ?

so outside the conductor do i just use the E=q/4(pi)e0R^2 ?
It's not correct. What is area of Gaussian surface?

ahhh so i need to use the area of a cylinder? so 2(pi)rh +2(pi)r^2 ?