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# 1: Electric Fields


So, you might ask, if your primary interest in electricity is to understand how machines, instruments and electrical equipment work, is there any point in studying electricity from the very “academic” and abstract approach that will be used in these notes, completely divorced as they appear to be from the world of practical reality? The answer is that electrical engineers more than anybody must understand the basic scientific principles before they even begin to apply them to the design of practical appliances. So – do not even think of electrical engineering until you have a thorough understanding of the basic scientific principles of the subject.

• 1.1: Prelude to Electric Fields
The subject of electromagnetism is an amalgamation of what were originally studies of three apparently entirely unrelated phenomena, namely electrostatic phenomena of the type demonstrated with pieces of amber, pith balls, and ancient devices such as Leyden jars and Wimshurst machines; magnetism, and the phenomena associated with lodestones, compass needles and Earth’s magnetic field; and current electricity – the sort of electricity generated by chemical cells such as Daniel and Leclanché cells
• 1.2: Triboelectric Effect
It was long ago noticed that if a sample of amber is rubbed with cloth, the amber became endowed with certain apparently wonderful properties. For example, the amber would be able to attract small particles of fluff to itself. The effect is called the triboelectric effect. The amber, after having been rubbed with cloth, is said to bear an electric charge, and space in the vicinity of the charged amber within which the amber can exert its attractive properties is called an electric field.
• 1.3: Experiments with Pith Balls
There are two kinds of electric charge, with exactly opposite properties. We observe that like charges (i.e. those of the same sign) repel each other, and unlike charges (i.e. those of opposite sign) attract each other.
• 1.4: Experiments with a Gold-leaf Electroscope
A gold-leaf electroscope has a vertical rod R attached to a flat metal plate. Electroscopes detect electric charge by the motion of a test object due to the Coulomb electrostatic force. Since the electric potential or voltage of an object with respect to ground equals its charge divided by its capacitance to ground, an electroscope can be regarded as a crude voltmeter.
• 1.5: Coulomb's Law
Coulomb’s Law is that two electric charges of like sign repel each other with a force that is proportional to the product of their charges and inversely proportional to the square of the distance between them:
• 1.6: Electric Field E
The region around a charged body within which it can exert its electrostatic influence may be called an electric field. In principle, it extends to infinity, but in practice it falls off more or less rapidly with distance.
• 1.7: Electric Field D
We have been assuming that all “experiments” described have been carried out in a vacuum or (which is almost the same thing) in air. But what if the point charge, the infinite rod and the infinite charged sheet of Section 1.6 are all immersed in some medium whose permittivity is not ϵ0 , but is instead ϵ ?
• 1.8: Flux
The product of electric field intensity and area is the flux . Whereas E is an intensive quantity, flux is an extensive quantity.
• 1.9: Gauss's Theorem
Gauss’s theorem argues that the total normal component of the D -flux through any closed surface is equal to the charge enclosed by that surface.  It is a natural consequence of the inverse square nature of Coulomb’s law.

Thumbnail: The electric field lines and equipotential lines for field of two point charges. (CC BY-SA 3.0; Geek3 via Wikipedia).

This page titled 1: Electric Fields is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.