Electric field between inner and outer cylinder

[Brennen berkley]

Homework Statement

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.

Homework Equations

E = q/εA

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.

 

[Charles Link]

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.

 

[Qwertywerty]

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.

What exactly do you want to know? If, whether the field for r less than 1, or greater than 1.25cm is zero, then yes, it would be.