How Do You Apply Zonal Spherical Harmonics in Electromagnetism Problems?

AI Thread Summary
The discussion focuses on applying Zonal Spherical Harmonics to solve electromagnetism problems, particularly involving boundary conditions where the potential is zero on a sphere and at infinity. Participants express difficulty in finding solutions and understanding how to incorporate Zonal Spherical Harmonics into their calculations. It is suggested to analyze the boundary conditions and equate the potential at the sphere's surface to zero. Additionally, it's noted that only the constant term contributes at infinity due to the lack of dependence on the angle. Overall, the conversation emphasizes the importance of boundary conditions in utilizing Zonal Spherical Harmonics effectively.
Zaitul Hidayat
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I don't really understand how to find the solution. I've tried to find the solution in books and google but still can't find it. In general, the Question 1 the problem is using the method of Image charge and Induced surface charge density. but this time my professor changed it to something else. can you guys help me? Thank You.

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Which books have you searched for a solution to problem 1?
 
But you can do this exercise by noticing the boundary condition: ##\varphi=0## on the sphere and ##\varphi=0## at infinity; and plugging the Zonal Spherical Harmonics.
 
MathematicalPhysicist said:
Which books have you searched for a solution to problem 1?
I'm not sure which book I read, because I just googled it. and I found some questions that are very similar but only different methods are used.
 
MathematicalPhysicist said:
But you can do this exercise by noticing the boundary condition: ##\varphi=0## on the sphere and ##\varphi=0## at infinity; and plugging the Zonal Spherical Harmonics.
but I still don't understand how I plugged the Zonal Spherical Harmonics into it :cry:
 
Zaitul Hidayat said:
but I still don't understand how I plugged the Zonal Spherical Harmonics into it :cry:
At ##r=R## you get ##\varphi(R,\theta)=0##, plug ##r=R## into the Zonal Spherical harmonic and equate to zero. For ##\varphi(r=\infty,\theta)=0##, notice that only ##P_0(\cos\theta)## contribution here, since there's no dependence on ##\cos \theta## in the boundary conditions.
 
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