By Seares F. H., van Maanen A., Ellerman F.
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Extra info for The location of the sun's magnetic axis
Note that as you walk around the yellow loop the magnetic field always points in roughly the G G same direction as the path: v B ∫ ⋅ d s ≠ 0 , whereas around the red loop sometimes the field points with you, sometimes G G against you: v∫ B ⋅ d s = 0 . We use Ampere’s law in a very similar way to how we used Gauss’s law. For highly symmetric current distributions, we know that the produced magnetic field is constant along certain paths. For example, in the picture above the magnetic field is constant around any blue circle.
0 by symmetry). This is a crucial step since it lets you turn the integral into a simple multiplication. G G 5) Calculate v∫ B ⋅ d s . (Path Length) (summed on each side for rectangular loops). Don’t forget that it is a dot product, so that if B is perpendicular to your path the integral is zero. 6) Finally, determine the current punching through your Amperian loop. Often this is just a matter of counting how many wires carrying current I pass through your loop. Sometimes it is slightly more complicated, involving integration of the current density: G G I = ∫∫ J ⋅ d A 7) Equate and solve for the magnitude of B.
The current in loop 1 produces a magnetic field (and hence flux) through loop 2. If that current changes in time, the flux through 2 changes in time, creating an EMF in loop 2. The mutual inductance, M, depends on geometry, both on how well the current in the first loop can create a magnetic field and on how much magnetic flux Summary for Class 21 p. 02 Wednesday 3/30/05 / Thursday 3/31/05 through the second loop that magnetic field will create. Interestingly, mutual inductance is symmetric – if you flip the subscripts in the above equation, it remains true.
The location of the sun's magnetic axis by Seares F. H., van Maanen A., Ellerman F.