coulombslaw

# coulombslaw - Chapter 2 Coulombs Law 2.1 Electric Charge....

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Chapter 2 Coulomb’s Law 2.1 Electric Charge. .................................................................................................... 2-3 2.2 Coulomb's Law . ................................................................................................... 2-3 Animation 2.1: Van de Graaff Generator. .............................................................. 2-4 2.3 Principle of Superposition. ................................................................................... 2-5 Example 2.1: Three Charges. ................................................................................... 2-5 2.4 Electric Field. ....................................................................................................... 2-7 Animation 2.2: Electric Field of Point Charges . .................................................... 2-8 2.5 Electric Field Lines. ............................................................................................. 2-9 2.6 Force on a Charged Particle in an Electric Field . .............................................. 2-10 2.7 Electric Dipole . .................................................................................................. 2-11 2.7.1 The Electric Field of a Dipole. ..................................................................... 2-12 Animation 2.3: Electric Dipole. ............................................................................ 2-13 2.8 Dipole in Electric Field. ..................................................................................... 2-13 2.8.1 Potential Energy of an Electric Dipole . ....................................................... 2-14 2.9 Charge Density. .................................................................................................. 2-16 2.9.1 Volume Charge Density. .............................................................................. 2-16 2.9.2 Surface Charge Density . .............................................................................. 2-17 2.9.3 Line Charge Density . ................................................................................... 2-17 2.10 Electric Fields due to Continuous Charge Distributions. ................................... 2-18 Example 2.2: Electric Field on the Axis of a Rod . ................................................ 2-18 Example 2.3: Electric Field on the Perpendicular Bisector. .................................. 2-19 Example 2.4: Electric Field on the Axis of a Ring . ............................................... 2-21 Example 2.5: Electric Field Due to a Uniformly Charged Disk. ........................... 2-23 2.11 Summary. ........................................................................................................... 2-25 2.12 Problem-Solving Strategies . .............................................................................. 2-27 2.13 Solved Problems . ............................................................................................... 2-29 2.13.1 Hydrogen Atom . ....................................................................................... 2-29 2.13.2 Millikan Oil-Drop Experiment . ................................................................ 2-30 2.13.3 Charge Moving Perpendicularly to an Electric Field . .............................. 2-31 2.13.4 Electric Field of a Dipole. ......................................................................... 2-33 2-1

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2.13.5 Electric Field of an Arc. ............................................................................ 2-36 2.13.6 Electric Field Off the Axis of a Finite Rod. .............................................. 2-37 2.14 Conceptual Questions . ....................................................................................... 2-39 2.15 Additional Problems . ......................................................................................... 2-40 2.15.1 Three Point Charges. ................................................................................. 2-40 2.15.2 Three Point Charges. ................................................................................. 2-40 2.15.3 Four Point Charges . .................................................................................. 2-41 2.15.4 Semicircular Wire. .................................................................................... 2-41 2.15.5 Electric Dipole . ......................................................................................... 2-42 2.15.6 Charged Cylindrical Shell and Cylinder. .................................................. 2-42 2.15.7 Two Conducting Balls . ............................................................................. 2-43 2.15.8 Torque on an Electric Dipole. ................................................................... 2-43 2-2
Coulomb’s Law 2.1 Electric Charge There are two types of observed electric charge, which we designate as positive and negative. The convention was derived from Benjamin Franklin’s experiments. He rubbed a glass rod with silk and called the charges on the glass rod positive. He rubbed sealing wax with fur and called the charge on the sealing wax negative. Like charges repel and opposite charges attract each other. The unit of charge is called the Coulomb (C). The smallest unit of “free” charge known in nature is the charge of an electron or proton, which has a magnitude of (2.1.1) 19 1.602 10 C e Charge of any ordinary matter is quantized in integral multiples of e . An electron carries one unit of negative charge, , while a proton carries one unit of positive charge, e e + . In a closed system, the total amount of charge is conserved since charge can neither be created nor destroyed. A charge can, however, be transferred from one body to another. 2.2 Coulomb's Law Consider a system of two point charges, and , separated by a distance in vacuum. The force exerted by on is given by Coulomb's law: 1 q 2 q r 1 q 2 q 12 12 2 ˆ e qq k r = Fr G (2.2.1) where is the Coulomb constant, and e k ˆ / r = rr G is a unit vector directed from to , as illustrated in Figure 2.2.1(a).

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## This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.

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coulombslaw - Chapter 2 Coulombs Law 2.1 Electric Charge....

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