20 pts
An infinitely long solid insulating cylinder with radius, a, has positive charge uniformly distributed throughout it with a constant charge per unit volume, Ïv.
1. Using Gauss's law, derive the expression for the electric field inside the cylinder.
2. Using Gauss's law, derive the expression for the electric field outside the cylinder.
3. 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 cylinder's volume density, Ïv, and the line density, Ï?