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where is the magnetic force constant from the Biot–Savart law, / is the total force on either wire per unit length of the shorter (the longer is approximated as infinitely long relative to the shorter), is the distance between the two wires, and , are the direct currents carried by the wires.
In electrical engineering, electrical length is a dimensionless parameter equal to the physical length of an electrical conductor such as a cable or wire, divided by the wavelength of alternating current at a given frequency traveling through the conductor. [1] [2] [3] In other words, it is the length of the conductor measured in wavelengths.
The electrical resistance of a uniform conductor is given in terms of resistivity by: [40] = where ℓ is the length of the conductor in SI units of meters, a is the cross-sectional area (for a round wire a = πr 2 if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
The strength of the field at any point is inversely proportional to the distance of the point from the wire. This sparked a great deal of research into the relation between electricity and magnetism. André-Marie Ampère investigated the magnetic force between two current-carrying wires, discovering Ampère's force law .
Joule immersed a length of wire in a fixed mass of water and measured the temperature rise due to a known current through the wire for a 30 minute period. By varying the current and the length of the wire he deduced that the heat produced was proportional to the square of the current multiplied by the electrical resistance of the wire.
The formula to calculate the area in circular mil for any given AWG (American Wire Gauge) size is as follows.represents the area of number AWG. = (() /) For example, a number 12 gauge wire would use =:
(E.g. 1 mm diameter wire is ~18 AWG, 2 mm diameter wire is ~12 AWG, and 4 mm diameter wire is ~6 AWG). This quadruples the cross-sectional area and conductance. A decrease of ten gauge numbers (E.g. from 12 AWG to 2 AWG) multiplies the area and weight by approximately 10, and reduces the electrical resistance (and increases the conductance ) by ...