Two long straight parallel wires

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Magnetostatics

Electricity, Magnetism and Electromagnetism, Ch Ampère's law, magnetic flux and the shape of the magnetic field

Problem

Two long straight parallel wires,

3.0\,\mathrm{cm}

apart, each carry a steady current of

4.0\,\mathrm{A}

in the same direction. A student wants the field at

5.0\,\mathrm{cm}

from the midpoint between them. She draws a circle of radius

s = 5.0\,\mathrm{cm}

in a plane perpendicular to the wires, centred on the midpoint of the line joining them, so that the circle encloses both wires, and writes: "Ampère's law:

B\,2\pi s = \mu_0(2I)

, so

B = \dfrac{\mu_0(8.0\,\mathrm{A})}{2\pi(0.050\,\mathrm{m})} = 3.2\times10^{-5}\,\mathrm{T}

at every point of the circle." ((a)) Identify the step that is wrong and say exactly which condition on the loop fails. ((b)) State the one quantity her loop does give correctly, and evaluate it with its unit.

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