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A very long, solid insulating cylinder with radius R has a cylindrical hole with radius a bored along its entire length. The axis of the hole is a distance b from the axis of the cylinder, where a<b<R (as shown in figure). The solid material of the cylinder has a uniform has a uniform volume charge density ρ. Find the magnitude and direction of the electric field inside the hole, and show that this is uniform over the entire hole.
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Solution
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Ewhole=EcylinderEhole
Ewhole=ρr2ϵ0ρS2ϵ0=ρ2ϵ0(rs)=ρ2ϵ0b
Note that Ewhole is uniform within the hole.
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