2: The Electric Field
- Page ID
- 48117
\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)
The ancient Greeks observed that when the fossil resin amber was rubbed, small light-weight objects were attracted. Yet, upon contact with the amber, they were then repelled. No further significant advances in the understanding of this mysterious phenomenon were made until the eighteenth century when more quantitative electrification experiments showed that these effects were due to electric charges, the source of all effects we will study in this text.
- 2.1: Electric Charge
- We now know that all matter is held together by the attractive force between equal numbers of negatively charged electrons and positively charged protons.
- 2.2: The Coulomb Force Law Between Stationary Charges
- It remained for Charles Coulomb in 1785 to express these experimental observations in a quantitative form. He used a very sensitive torsional balance to measure the force between two stationary charged balls as a function of their distance apart.
- 2.3: Charge Distributions
- The method of superposition used in Section 2.2.4 will be used throughout the text in relating fields to their sources.
- 2.4: Gauss's Law
- We could continue to build up solutions for given charge distributions using the coulomb superposition integral of Section 2.3.2. However, for geometries with spatial symmetry, there is often a simpler way using some vector properties of the inverse square law dependence of the electric field.
- 2.5: The Electric Potential
- If we have two charges of opposite sign, work must be done to separate them in opposition to the attractive coulomb force. This work can be regained if the charges are allowed to come together.
- 2.6: The Method of Images with Line Charges and Cylinders
- The potential of an infinitely long line charge \(\lambda\) is given in Section 2.5.4 when the length of the line L is made very large. More directly, knowing the electric field of an infinitely long line charge from Section 2.3.3 allows us to obtain the potential by direct integration:
- 2.7: The Method of Images with Point Charges and Spheres
- A point charge q is a distance D from the center of the conducting sphere of radius R at zero potential as shown in Figure 2-27a.
Thumbnail: The electric field lines and equipotential lines for field of two point charges. (CC BY-SA 3.0; Geek3 via Wikipedia).