Abampere: Difference between revisions
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In [[physics]], the '''abampere''', symbol abA, is the unit of electric current in the cgs-emu (centimeter-gram-second electromagnetic) system of units | In [[physics]], the '''abampere''', symbol abA, is the unit of electric current in the cgs-emu (centimeter-gram-second electromagnetic) system of units: | ||
: 1 abA = 10 A ([[ampere (unit)|ampere]]). | |||
Its definition is based on [[Ampere's equation#Two straight, infinite, and parallel wires|Ampère's equation]] in cgs-emu units: | |||
:<math> | :<math> | ||
\frac{F}{l} = \frac{2 i^2}{r} | \frac{F}{l} = \frac{2 i^2}{r}. | ||
</math> | </math> | ||
By definition, the abampere is the constant current ''i'' which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed ''r'' = 1 cm apart in vacuum, would produce between these conductors a force ''F'' equal to 2 [[dyne]] per length ''l'' = 1 cm in each of the two wires. | |||
The abampere is not used much anymore, but is needed in some definitions in the cgs-emu system of units. | |||
The connection between abampere and ampere follows from the following reasoning, where it is used that 1 dyn = 1⋅10<sup>−5</sup> [[newton]]: | |||
The SI definition states that two currents, each of one ampere, running through wires that are one meter apart give a force of 2⋅10<sup>−7</sup> N = 2⋅10<sup>−2</sup> dyn per meter of wire. Two wires, one cm apart, give the same force (0.02 dyn) per cm of wire, since Ampère's equation is invariant under scaling of ''r'' and ''l'' by the same factor. In the cgs-emu definition, two currents, each of one abampere, running through wires that are one cm apart give a force of 2 dyn per cm of wire. The cgs-emu definition gives a standard force that is 100 times larger than the corresponding SI standard force (both are expressed in cm). Since the currents are contained quadratically in Ampère's equation, it follows that the current in the cgs-emu definition is 10 times larger than in the SI definition, or 1 abA = 10 A. | |||
Latest revision as of 09:18, 8 July 2008
In physics, the abampere, symbol abA, is the unit of electric current in the cgs-emu (centimeter-gram-second electromagnetic) system of units:
- 1 abA = 10 A (ampere).
Its definition is based on Ampère's equation in cgs-emu units:
By definition, the abampere is the constant current i which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed r = 1 cm apart in vacuum, would produce between these conductors a force F equal to 2 dyne per length l = 1 cm in each of the two wires.
The abampere is not used much anymore, but is needed in some definitions in the cgs-emu system of units.
The connection between abampere and ampere follows from the following reasoning, where it is used that 1 dyn = 1⋅10−5 newton:
The SI definition states that two currents, each of one ampere, running through wires that are one meter apart give a force of 2⋅10−7 N = 2⋅10−2 dyn per meter of wire. Two wires, one cm apart, give the same force (0.02 dyn) per cm of wire, since Ampère's equation is invariant under scaling of r and l by the same factor. In the cgs-emu definition, two currents, each of one abampere, running through wires that are one cm apart give a force of 2 dyn per cm of wire. The cgs-emu definition gives a standard force that is 100 times larger than the corresponding SI standard force (both are expressed in cm). Since the currents are contained quadratically in Ampère's equation, it follows that the current in the cgs-emu definition is 10 times larger than in the SI definition, or 1 abA = 10 A.