How Do You Apply Zonal Spherical Harmonics in Electromagnetism Problems?

In summary, the speaker expresses difficulty in finding the solution to a problem using the method of Image charge and Induced surface charge density. They have searched for a solution in various books and through Google, but have not been successful. The speaker's professor has changed the method for this problem, and they are seeking assistance. In response, they are advised to consider the boundary conditions and use Zonal Spherical Harmonics. The speaker still does not understand how to apply this method and expresses frustration.
  • #1
Zaitul Hidayat
3
0
Thread moved from the technical forums to the schoolwork forums
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.

Question 1.png


Question 2.png

Question 3.png
 
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  • #2
Which books have you searched for a solution to problem 1?
 
  • #3
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.
 
  • #4
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.
 
  • #5
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:
 
  • #6
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.
 

FAQ: How Do You Apply Zonal Spherical Harmonics in Electromagnetism Problems?

1. What is classical electromagnetism?

Classical electromagnetism is a branch of physics that studies the relationship between electric and magnetic fields, and their interactions with matter. It is based on the laws of electromagnetism developed by James Clerk Maxwell in the 19th century.

2. What are the fundamental equations of classical electromagnetism?

The fundamental equations of classical electromagnetism are Maxwell's equations, which describe the behavior of electric and magnetic fields. They include Gauss's law, which relates electric fields to electric charges, and Ampere's law, which relates magnetic fields to electric currents.

3. How does classical electromagnetism explain the behavior of light?

Classical electromagnetism explains light as an electromagnetic wave, with oscillating electric and magnetic fields perpendicular to each other. This theory was first proposed by Maxwell and has been supported by numerous experiments, such as the double-slit experiment.

4. What are some practical applications of classical electromagnetism?

Classical electromagnetism has many practical applications, including the generation and transmission of electricity, the operation of electronic devices, and the development of technologies such as radios, televisions, and computers. It is also used in medical imaging techniques such as MRI and in the study of materials through techniques like X-ray diffraction.

5. How does classical electromagnetism relate to other branches of physics?

Classical electromagnetism is closely related to other branches of physics, such as classical mechanics and quantum mechanics. It provides a framework for understanding the behavior of charged particles and their interactions with electric and magnetic fields. It also plays a crucial role in the development of modern physics, as it was a major inspiration for the development of quantum mechanics.

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