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Discharging a magnetized sphere
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[QUOTE="TSny, post: 4964323, member: 229090"] Your work is very nicely done. The integration constant can be determined by considering what K must be at ##\theta = \pi/2##. Consider the net current flowing out of the southern hemisphere and the [I]net[/I] current flowing [I]out[/I] of the northern hemisphere. How should these compare? If you can see that K must go to zero at the south pole, then that would be an easy way to get the integration constant. My intuition wasn't good enough to be confident about dealing with this point of the sphere. When I see the surface current expressed as ##K = \frac{dI}{dl_\perp}##, I'm with you. I think of it as division rather than a derivative. To interpret it as a derivative you could do something like the following. Imagine a curve in the surface that’s drawn perpendicular to the current flow. Let the starting point of the curve be O. Let ##s## be arc length along the curve measured from O. Consider the function ##I(s)## that gives the total current crossing the curve between O and the point at arc distance ##s##. Then the surface current density at ##s## is ##K = \frac{dI(s)}{ds}##, where here we actually have a derivative of a function. But, I don’t think this is a common way of looking at it. [/QUOTE]
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