Surface current on a spherical superconductor

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The discussion centers on a query regarding part b of a problem related to surface current on a spherical superconductor. The original poster seeks validation for their solution. Another participant confirms that the work appears correct. The exchange emphasizes the importance of peer review in understanding complex physics concepts. Overall, the conversation highlights collaborative problem-solving in advanced topics.
gausswell
Homework Statement
Find the surface current on a spherical superconductor.
Relevant Equations
K=sigma * v
I need help with part b.
21926439f11214bdb3d781885d057ff2.png

My solution:
e632f985b3cb7405287859652045a98d.png

Have I done it right?
 
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gausswell said:
Have I done it right?
Your work looks right to me.
 
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Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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