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Solved: A very long, solid insulating cylinder has radius
Chapter 22, Problem 62P(choose chapter or problem)
A very long, solid insulating cylinder with radius has a cylindrical hole with radius bored along its entire length. The axis of the hole is a distance from the axis of the cylinder, where (Fig. P22.62). The solid material of the cylinder has a uniform volume charge density Find the magnitude and direction of the electric field \(\bar{E}\) inside the hole, and show that \(\bar{E}\) is uniform over the entire hole. (Hint: See Problem 22.61.)
Equation transcription:
Text transcription:
bar{E}
Questions & Answers
QUESTION:
A very long, solid insulating cylinder with radius has a cylindrical hole with radius bored along its entire length. The axis of the hole is a distance from the axis of the cylinder, where (Fig. P22.62). The solid material of the cylinder has a uniform volume charge density Find the magnitude and direction of the electric field \(\bar{E}\) inside the hole, and show that \(\bar{E}\) is uniform over the entire hole. (Hint: See Problem 22.61.)
Equation transcription:
Text transcription:
bar{E}
ANSWER:Solution 62P
Step 1
Consider that according to Gauss law, the electric field at point inside the cylinder in x-y plane and in the radial direction.
…… (1)
Here, is the electric field vector, is the position vector in the x-y plane, is the charge density, and is the permittivity of free space.
Substitute, for .
If the cylinder axis goes through point in the x-y plane, then electric field off-axis is given as.
Here, is the axis- off position vector and is the electric field vector at off-axis.