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Name: Huang
Status: student
Age: 18
Location: N/A
Country: N/A
Date: 1999
Question:
Does Ampere's law (for steady currents) somehow assume the magnetic field of an infinitely long line of current as opposed to just a current element? Specifically, the magnetic field produced by just one infinitesimal current element alone (with no other current elements present in space) drops off in strength as 1/r^2, so it seems incompatible with Ampere's law if one chooses certain paths in a plane perpendicular to the current element. Why is this so?

No. Ampere's law relates the current passing through an area to the line integral of the magnetic field over the perimeter of the area. Sure, the field drops off as 1/r^2, but the distance over which the line integral is taken increases as r^2. So it doesn't matter where you draw the perimeter. You'll always get the same answer if the current is completely bounded by the perimeter.

Tim Mooney


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