# Homework Help: Electric field between inner and outer cylinder

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1. Mar 3, 2016

### Brennen berkley

1. The problem statement, all variables and given/known data
A capacitor is constructed of two long concentric metal cylinders, each having length of 1.0 meters. The inner cylinder has a radius R1 = 1.0 cm, and the outer cylinder has a radius R2 = 1.25 cm. The hollow space between the two cylinders is filled with nylon having a dielectric constant of 4.0. A charge of Q =5 nC is transferred from the inner cylinder to the outer shell. (a) Find the field between the two using Gauss's law, and use the computer to make a graph of the magnitude of the electric field E(r) from r = 0.5 cm to r = 1.5 cm.

2. Relevant equations
E = q/εA

3. The attempt at a solution
The field on the inner cylinder would be E = 8990 N/C and the field on the outer cylinder would be 7190 N/C. I am confused though because it is asking for an electric field between the plates. Do they just want an equation for the field based on r? For the graph part I assume they want an equation, but when r < 1 or r > 1.25 the field would be zero right? I just don't totally understand the question, so any input regarding what you think my professor wants would be appreciated.

I am also assuming the cylinders have no top or bottom.

2. Mar 3, 2016

To begin, first work the problem without any dielectric between the cylinders. A charge per unit length Q/L gives a radially outward electric field (using Gauss's law M.K.S. units) obeying $E(r)*2*\pi*r*L=(Q/L)/\epsilon_o)*L$ ==>> $E(r)=(Q/L)/(2\pi*r\epsilon_o)$ The dielectric will reduce this E(r) by a factor of the dielectric constant $\epsilon$. The electric field is zero outside of the region $1.0 cm<r<1.25 cm$ In doing the calculations, be sure to have "r" expressed in meters.