Define the Ampere: Force/Length = 2*10-7N/m

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SUMMARY

The discussion focuses on defining the ampere through the interaction of two parallel wires carrying current. The force per unit length between the wires is expressed as F/length = μ₀I²/2πd, where μ₀ represents the permeability of free space. At a separation of 1 meter, the force is quantified as F = 2 × 10⁻⁷I². The conclusion drawn is that if two long parallel wires 1 meter apart carry equal currents and experience a force of 2 × 10⁻⁷ N, the current is defined to be 1 ampere.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically the interaction of currents.
  • Familiarity with the concept of force per unit length in physics.
  • Knowledge of the permeability of free space (μ₀) and its significance in electromagnetism.
  • Basic algebra for manipulating equations and solving for variables.
NEXT STEPS
  • Study the derivation of the force between parallel current-carrying wires in detail.
  • Learn about the significance of the permeability of free space (μ₀) in electromagnetic calculations.
  • Explore practical applications of the ampere in electrical engineering.
  • Investigate the relationship between current, voltage, and resistance in circuits using Ohm's Law.
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Physics students, electrical engineers, and anyone interested in understanding the fundamental definitions of electrical units and their applications in electromagnetism.

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Homework Statement


Two very long, thin, straight, parallel wires each carrying a current I in the same direction are separated by a distance, d. With the aid of a diagram which indicates the current directions, account for the force on each wire and show on the diagram the direction of one of the forces. Write an expression for the magnitude of the force per unit length of wire and hence define the ampere.


Homework Equations





The Attempt at a Solution


did necessary steps to get to force/length=uoI2/2pi*d
then at 1m separation F=2*10-7I2
From text: "if two long parallel wires 1m apart carry equal currents and experience a force of of 2*10-7N then the current is defined to be 1Ampere"
I think I am pretty close to the answer but I have a force of 2*10-7I2 -how do I get rid of the I2?
 
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You are defining the Ampere, so I= 1 A.
 
thanks I thought it would be something simple like that...
 

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