8.02 Lecture Notes - Lecture 1: Current Density, Negative Number
Document Summary
Integrating b around the loop shown gives us is zero. Calculate the line integral of magnetic eld b ds about a circular path of radius r centered on the wire for a very long current carrying wire. Current enclosed is the ux of the current density through an open surface s bounded by the closed path. Because the unit normal to an open surface is not uniquely de ned, this expression is unique up to a plus or minus sign. B s = j n a. In order to have a non-zero line integral of magnetic eld around a closed path, there must be current punching through any area with path as boundary. B ds = 0 for no enclosed current. Integrating b around the loop in the clockwise direction shown gives us a negative number. It is useful to calculate magnetic eld for some sources with enough symmetry in which there exists a closed path such that.
