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electrostatic unit

 
Dictionary: electrostatic unit

n. (Abbr. esu)
Any unit of electricity or magnetism in the centimeter-gram-second system based on the forces of interaction between electric charges.


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Measures and Units: electrostatic unit
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ES unit, e.s. unit

Metric-c.g.s. The various units of the e.s.u. system have specific names obtained by prefixing more familiar names with ‘stat’, but are often referred to purely descriptively as the ‘e.s. unit of capacitance’, etc. The relevant units are, by subject and showing both distinct name and the SI equivalent of value, one e.s. unit of:

capacitancestatfarad= 1.112 650~ pF
electric chargestatcoulomb= 333.5641~ pC
electric conductancestatmho= 1.112 650~ pS
electric currentstatampere= 333.5641~ pA
electric potentialstatvolt= 299.7925~ V
electric resistancestatohm= 898.7552~ TΩ
inductancestathenry= 898.7552~ TH
magnetomotive forcestatampere·turn= 3.335 641~ × 10-10 A·turn
For the numeric values deriving from c, the speed of light: see e.s.u. system.

WordNet: electrostatic unit
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Note: click on a word meaning below to see its connections and related words.

The noun has one meaning:

Meaning #1: any of various units of electricity based on forces of interaction between electric charges


Wikipedia: Statcoulomb
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The statcoulomb (statC) or franklin (Fr) or electrostatic unit of charge (esu) is the physical unit for electrical charge used in the centimetre-gram-second (cgs) electrostatic system of units. It is a derived unit given by

1 statC = 1 g1/2 cm3/2 s−1 = 1 erg1/2 cm1/2.

The SI system of units uses the coulomb (C) instead. The conversion is

1 C = 2997924580 statC.

This equation is exact (however, see below for a warning on how to properly apply it). The number on the right-hand side is 10 times the value of the speed of light expressed in meters/second. The approximate conversions in both directions are:

1 C ≈ 2.99792×109 statC,
1 statC ≈ 3.33564×10−10 C.

The statcoulomb is defined as follows: if two stationary objects each carry a charge of 1 statC and are 1 cm apart, they will electrically repel each other with a force of 1 dyne. This repulsion is governed by Coulomb's law, which in the Gaussian-cgs system states:

F=\frac{q_1q_2}{r^2}

where F is the force, q1 and q2 are the two charges, and r is the distance between the charges. Performing dimensional analysis on Coulomb's law, the dimension of electrical charge in cgs must be [mass]1/2 [length]3/2 [time]-1. (This statement is not true in SI units; see below.) We can be more specific in light of the definition above: Plugging in F=1 dyne, q1=q2=1 statC, and r = 1 cm, we get:

1 statC = g1/2 cm3/2 s−1

as expected.

The coulomb is an extremely large charge rarely encountered in electrostatics, while the statcoulomb is closer to everyday charges.

Dimensional relation between Statcoulomb and Coulomb

In the cgs-Gaussian unit system, as mentioned above, Coulomb's law states

F=\frac{q_1q_2}{r^2}

To be consistent with this equation, the statcoulomb must be (and is) dimensionally equivalent to [mass]1/2 [length]3/2 [time]−1.

On the other hand, in SI units, Coulomb's law is different:

F=\frac{q_1q_2}{4\pi\epsilon_0 r^2}

Since ε0, the vacuum permittivity, is not dimensionless, the coulomb (the SI unit of charge) is not dimensionally equivalent to [mass]1/2 [length]3/2 [time]−1, unlike the statcoulomb. In fact, it is impossible to express the Coulomb in terms of mass, length, and time alone.

Consequently, the statement 1 C = 2997924580 statC must be interpreted with caution: the units on the two sides are not consistent. Given a formula, one cannot simply use this conversion factor to switch between Coulombs and statcoulombs, as one would freely switch between centimeters and meters. Rather, this statement should be understood as: "1 coulomb corresponds to 2997924580 statcoulombs"; in other words, if a physical object has a charge of 1 coulomb, it also has a charge of 2997924580 statcoulombs.

On the other hand, the following conversion is fully dimensionally consistent, and often useful for switching between SI and cgs formulae:

1 \; \mathrm{C}/\sqrt{4 \pi \epsilon_0} = 2997924580 \; \mathrm{statC}

where ε08.85×10−12 A2 s4kg−1m−3 = 8.85×10−21 A2s4g−1cm−3.


 
 

 

Copyrights:

Dictionary. The American Heritage® Dictionary of the English Language, Fourth Edition Copyright © 2007, 2000 by Houghton Mifflin Company. Updated in 2009. Published by Houghton Mifflin Company. All rights reserved.  Read more
Measures and Units. A Dictionary of Weights, Measures, and Units. Copyright © Donald Fenna 2002, 2004. All rights reserved.  Read more
WordNet. WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Statcoulomb" Read more