Question

An infinitely long, solid insulating cylinder with radius a has positive charge uniformly distributed throughout it with a constant charge per unit volume p.
a) using Gauss's law, derive the expression for the electric field inside the cylinder r<a from the axis of the cylinder in terms of the charge density p.
b) now when r>a
c) Explain how your results show that the electric field created by the solid cylinder is identical to that of the infinite line of charge for points outside of the cylinder. What is the relationship between the cylinders volume density p and the line density lambda.

Answer 1

I will be happy to check your work, I am uncertain where you are faltering on this.

Answer 2

I am uncertain on how to use gauss's law to derive the expression for the electric fields

Answer 3

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gaulaw.html
study that. Sally, flux is Electric field * surface area which is equal to totalenclosedcharge/epislon

so when you make a gaussian surface like a cylinder of length L and radius r...
E*L*PI*2r=totalenclosed charge/epislon

and total enclosed charge (for a spaced charge)= volumeenclosed*charge density.

Now outside the charged region, the total enclosed charge is just volume of the region( L*PI*a^2*charge density) and IT DOES NOT INCREASE.