Final answer:
When two parallel conductors carry currents in the same direction, they create magnetic fields that interact and cause an attractive force, which can be calculated by Ampere's Law. The force per unit length helps to define one ampere, which is the current that produces a specific force between two conductors.
Step-by-step explanation:
When two long straight parallel conductors carry steady current I₁ and I₂, separated by a distance d, and the currents are flowing in the same direction, they generate magnetic fields. These fields interact, producing an attractive force on each other. This is governed by the Right Hand Rule (RHR) which states that if the thumb of the right hand points in the direction of current flow, the curl of the fingers shows the direction of the magnetic field.
The strength of this magnetic field, represented by B, is given by the formula B = μI/2πd, where μ is the permeability of free space (4π x 10^-7 T.m/A) and d is the distance between the conductors. This results in Ampere's Law.
If wire 2 carries current I₂, then wire 1 feels a magnetic force due to the magnetic field created by wire 2. Using the formula for the force per unit length produced by the magnetic field on a current carrying wire, F₂/₂ = I₂B₁, we obtain the expression for the force, F₂₁ = μI₁I₂/2πd, which leads to the definition of one ampere: the current that, if maintained in two straight parallel conductors of infinite length and negligible cross-section, and placed 1 meter apart in a vacuum, would produce a force of 2 x 10^-7 newtons per meter of length.
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