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PhysicsRob

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## Homework Statement

A very long, solid insulating cylinder with radius "R" has a cylindrical hole with radius "a" bored along its entire length. The solid material of the cylinder has a uniform volume charge density "ρ". In this problem, you will find the magnitude and the direction of the electric field "E" inside the hole

(1) Find the magnitude and direction of the electric field of a cylinder similar to the one described above, but without the cylindrical hole.

(2) Find the magnitude and direction of the electric field inside the cylindrical hole when the cylindrical hole is in the center of the charged cylinder

(3)Find the magnitude and direction of the electric field inside the cylindrical hole when the center of the hole is a distance "b" from the center of the charged cylinder.

## Homework Equations

Gauss' Law

## The Attempt at a Solution

I solved through the first part for the solid cylinder by using a Gaussian cylinder with a radius of "r", r>R>a. I got that [itex]\vec{E}[/itex] = (R

^{2}ρ)/2rε

_{0}along vector "r". For the second part I thought that the field inside would be zero since if you drew a Gaussian cylinder inside the hole, wouldn't it contain no charge and thus have no electric field? For the third part I know that you need to use the idea of superposition, but I'm not really sure.