A cylinder of constant, positive charge density p and radius R has a cylindrical hole in it. The hole, of radius R/2 is not co-axial but centered at r = R/2 as in the diagram of the cross-section below. Find the electric field (magnitude and direction) at points A and B, both at r = R/2, but at different angles. Hint: A hole is really just a volume of no net charge that can be modeled as two overlapping volumes: one of positive charge density and one of negative charge density (but same magnitude).

A cylinder of constant, positive charge density p and radius R has a cylindrical hole in it. The hole, of radius R/2 is not co-axial but centered at r = R/2 as in the diagram of the cross-section below. Find the electric field (magnitude and direction) at points A and B, both at r = R/2, but at different angles. Hint: A hole is really just a volume of no net charge that can be modeled as two overlapping volumes: one of positive charge density and one of negative charge density (but same magnitude).

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Ising model of Ferromagnets

The Ising model is one of the easiest and most famous theoretical models for ferromagnetism in statistical mechanics. When a group of atomic spins aligns such that their magnetic moments are pointed in the same direction and produce a strong permanent magnetic moment in macroscopic size, the phenomenon is called ferromagnetism. The relative permeability of these magnets is greater than unity and increasing magnetization with the applied external field. Even in the absence of an external magnetic field, these substances retain spontaneous magnetization. An example of ferromagnets is iron.

Question

A cylinder of constant, positive charge density p and radius R has a cylindrical hole in it. The hole, of
radius R/2 is not co-axial but centered at r = R/2 as in the diagram of the cross-section below. Find the
electric field (magnitude and direction) at points A and B, both at r = R/2, but at different angles.
Hint: A hole is really just a volume of no net charge that can be modeled as two overlapping volumes:
one of positive charge density and one of negative charge density (but same magnitude).
B
R/2 R/2 R/2 R/2

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