Solved Griffiths Problem 3.28 - What to Conclude?

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In summary, the conversation discusses the agreement between the approximation and exact potential in Griffiths Problem 3.28. The question arises about higher multipoles and whether they are all identically zero or if they cancel out due to the charge distribution. The definition of a pure dipole is also clarified. Ultimately, it is determined that the field outside the sphere only has a dipole term in the expansion due to the P_1 distribution of charge. It is recommended to refer to Griffiths or other texts for definitions rather than relying on the web.
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ehrenfest
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[SOLVED] Griffiths Problem 3.28

Homework Statement


Please stop reading unless you have Griffiths E and M book.

In this problem, I found that the approximation agrees with the exact potential. I am not sure what to conclude about higher multipoles. Are they all identically zero or do they all cancel? Is there something about this charge distribution that makes that happen? Could I have predicted that without calculating it?


Homework Equations





The Attempt at a Solution

 
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  • #2
It is a pure dipole.
The cos\theta tells you it is pure P_1(cos\theta).
 
  • #4
That post gives the definition of a dipole used in elementary texts.
It describes one simple model of a dipole.
What I meant is that the field outside the sphere has only the dipole term as in the expansion. If you calculate the multipole moments of the sphere, you will find only a diple moment because of the P_1 dilstribution of charge.
Use Griffith's or some other text for definitions, not the web.
 

Related to Solved Griffiths Problem 3.28 - What to Conclude?

1. What is Griffiths Problem 3.28 and what does it involve?

Griffiths Problem 3.28 is a physics problem from the textbook "Introduction to Electrodynamics" by David J. Griffiths. It involves finding the electric potential inside and outside of a charge distribution using the method of separation of variables.

2. How do you approach solving Griffiths Problem 3.28?

The first step is to identify the boundary conditions and symmetry of the charge distribution. Then, we use the method of separation of variables to solve for the electric potential and apply boundary conditions to determine the constants of integration. Finally, we can draw conclusions based on the behavior of the electric potential.

3. What are the key concepts involved in solving Griffiths Problem 3.28?

The key concepts involved are the method of separation of variables, boundary conditions, and symmetry. Additionally, understanding the behavior of electric potential in various charge distributions is important.

4. What is the significance of solving Griffiths Problem 3.28?

Solving this problem helps us understand the behavior of electric potential in different charge distributions. It also reinforces the concept of separation of variables, which is a useful technique in solving various physics problems.

5. How can solving Griffiths Problem 3.28 be applied in real-world situations?

The concepts and techniques used in solving this problem can be applied in many real-world situations, such as studying the electric potential in electronic circuits or analyzing the electric field around conductors. It also has applications in fields such as electrochemistry and electromagnetism.

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