Book cover for University Physics with Modern Physics

University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

ISBN #9780072857368

1st Edition

3,117 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the core ideas of electric fields and Gauss’s Law. It introduces the concept of the electric field as a force per charge, discusses how to sum fields vectorially via the superposition principle, and shows how Gauss’s Law provides a powerful method for calculating electric fields when symmetry allows the selection of a convenient Gaussian surface. The material also covers the behavior of electric dipoles in fields, the idea of electrostatic shielding, and how charge distributions (whether point, line, surface, or volume) affect the electric field.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Definition: The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems.

The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems. •

Example Problems

Example 1

To be able to calculate the electric field created by a known distribution of charge using Gauss's Law, which of the following must be true? a) The charge distribution must be in a nonconducting medium. b) The charge distribution must be in a conducting medium. c) The charge distribution must have spherical or cylindrical symmetry. d) The charge distribution must be uniform. e) The charge distribution must have a high degree of symmetry that allows assumptions about the symmetry of its electric field to be made.

Example 2

An electric dipole consists of two equal and opposite charges situated a very small distance from each other. When the dipole is placed in a uniform electric field, which of the following statements is true? a) The dipole will not experience any net force from the electric field; since the charges are equal and have opposite signs, the individual effects will cancel out. b) There will be no net force and no net torque acting on the dipole. c) There will be a net force but no net torque acting on the dipole. d) There will be no net force, but there will (in general) be a net torque acting on dipole.

Example 3

A point charge, $+Q$, is located on the $x$ -axis at $x=a$, and a second point charge, $-Q$, is located on the $x$ -axis at $x=-a$. A Gaussian surface with radius $r=2 a$ is centered at the origin. The flux through this Gaussian surface is a) zero. b) greater than zero. c) less than zero. d) none of the above.

Example 4

A charge of $+2 q$ is placed at the center of an uncharged conducting shell. What will be the charges on the inner and outer surfaces of the shell, respectively? a) $-2 q,+2 q$ b) $-q,+q$ c) $-2 q,-2 q$ d) $-2 q,+4 q$

Example 5

Two infinite nonconducting plates are parallel to each other, with a distance $d=10.0 \mathrm{~cm}$ between them, as shown in the figure. Each plate carries a uniform charge distribution of $\sigma=4.5 \mu \mathrm{C} / \mathrm{m}^{2} .$ What is the electric field, $\vec{E}$ at point $P\left(\right.$ with $\left.x_{P}=20.0 \mathrm{~cm}\right) ?$ a) $0 \mathrm{~N} / \mathrm{C}$ b) $2.54 \hat{x} \mathrm{~N} / \mathrm{C}$ c) $\left(-5.08 \cdot 10^{5}\right) \hat{x} \mathrm{~N} / \mathrm{C}$ d) $\left(5.08 \cdot 10^{5}\right) \hat{x} \mathrm{~N} / \mathrm{C}$ e) $\left(-1.02 \cdot 10^{6}\right) \hat{x} \mathrm{~N} / \mathrm{C}$ f) $\left(1.02 \cdot 10^{6}\right) \hat{x} \mathrm{~N} / \mathrm{C}$
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