III. PROBLEM 3. MAGNETIC FIELD AND MAGNETIC POTENTIAL. Using the expression for the magnetic potential, А dl HO A- S d'
Posted: Fri Mar 04, 2022 10:16 am
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d calculate the potential of an infinite current carrying wire. The current is 1, the wire is placed along z-axis. Check that the curl of A gives the correct value for magnetic field B. Hints: 1. Take the integral. Make use of state that = In |z + Vz2 + a2| + const. = 2. Start from calculating magnetic potential at distance r from a very long, but finite wire that goes from -L to L, where L »r. Expand the resultant expression in logarithm into Taylor series up to r2/L” using V1+ a ~ 1+a/2, x«1, 1 / (2) 3. Does the constant term makes any physical sense? Does the physically meaningful part of the magnetic potential depend on the length of the wire? 4. Calculate magnetic field using this potential either in spherical coordinates or in Cartesian coordinates (for example, at the point (2,0,0)).