# Net charge and Electric field of a shell

## Homework Statement

A cylindrical shell of radius 7.00 cm and length 240 cm has it's charge uniformly distributed on it's curved surface. The magnitude of the electric field at a point 19.0cm radially outward from its axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the net charge on the shell and (b) the electric field at a point 4.00 cm from the axis, measured radially outward from the midpoint of the shell.

## Homework Equations

$$\Phi$$_E= $$\int$$E dA = qin/E_0

## The Attempt at a Solution

$$\Phi$$_E= E dA = qin/E_0
= E$$\int$$ dA = EA= $$\lambda$$l/E_0

E(2$$\Pi$$rl)= $$\lambda$$l/E_0

E= $$\lambda$$/2$$\Pi$$E_0r= 2k_e($$\lambda$$/r)

I'm not sure what else to do or if any of that is right.

## Answers and Replies

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Looks right, but your Latex is difficult to read. Your basically using Gauss' Law to find the electric field at points external to the cylinder. Your equation would be great if you knew the line charge density (lambda), but you don't. Use the relation that you used in your derivation to replace lambda with the charge q.