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A very long, solid insulating cylinder w...

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 at a distance b from the axis of the cylinder, where `altbltR` (as shown in figure). The solid material of the cylinder has a uniform volume charge density `rho`. 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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Text Solution

Verified by Experts

The correct Answer is:
`(rho)/( 2 epsilon_(0)) vec(b)`
`vecE _("whole") = vecE_("cylinder") - vecE_("hole")`
`= (rhovecr)/(2epsilon_0) - (rhovecs)/(2epsilon_0) = rho/(2epsilon_0) (vecr - vecs) = (rho)/(2epsilon_0) vecb`
Note that `vecE_(whole)` is uniform within the hole.
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