Solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9

In summary, the conversation discusses a problem in chapter 9 of DJ Griffith's electrodynamics, specifically problem 4. The problem asks to obtain equation 20 using the wave equation and separation of variables. The person asking for help is looking for a direct solution, but is advised to try and find the solution themselves by following two steps: writing down the wave equation and using the separation ansatz. They are also encouraged to learn the method of separation of variables for solving partial differential equations. The conversation ends with the person thanking those who responded to their post.
  • #1
Zeeshan Ahmad
Gold Member
24
9
Thread moved from the technical forums, and the OP has been reminded to show their work.
Homework Statement
Obtain eq 20(show in the below picture)
Directly from the waves equation by separation of variable
Relevant Equations
linear combinations of sinusoidal waves
While I was doing a problems of chapter 9 of DJ griffith electrodynamics

I came across this problem 4
Problem statement
Obtain eq 20(show in the below picture)
Directly from the waves equation by separation of variable
IMG_20210916_113300.jpg

Could I have a straight solution in your word
Thank you
 
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  • #2
No, but some help to find the solution yourself. Roughly speaking you just need to do two steps (which are always the same for such linear partial differential equations!):

(a) write down the wave equation
(b) write down the separation ansatz, plug it into the wave equation and find the corresponding mode functions
 
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Likes vela and berkeman
  • #3
Are you familiar with the method of separation of variables for solving PDEs? It's definitely something you should learn, if not.
 
  • #4
I have posted it in the morning and done it up till when I got response to it
But thanks for the response 😊
From mr vanhees and vela
 
Last edited:

1. What is Problem 4 of DJ Griffiths Electrodynamics Chapter 9?

Problem 4 of DJ Griffiths Electrodynamics Chapter 9 is a physics problem that involves finding the electric field inside and outside of a charged spherical shell with a cavity. It is a common problem in introductory electrodynamics courses.

2. What are the steps to solve Problem 4 of DJ Griffiths Electrodynamics Chapter 9?

The steps to solve Problem 4 of DJ Griffiths Electrodynamics Chapter 9 are as follows:

  • Draw a diagram of the system and label all known and unknown variables.
  • Apply Gauss's Law to find the electric field outside of the shell.
  • Use the boundary conditions to find the electric field inside the shell.
  • Solve for the charge distribution on the inner and outer surfaces of the shell.
  • Calculate the electric field inside the cavity using superposition.

3. What are the key concepts needed to solve Problem 4 of DJ Griffiths Electrodynamics Chapter 9?

To solve Problem 4 of DJ Griffiths Electrodynamics Chapter 9, one should have a good understanding of Gauss's Law, the concept of electric field, and the boundary conditions for electric fields at the surface of a conductor. Knowledge of vector calculus and basic algebra is also necessary.

4. What are some common mistakes when solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9?

Some common mistakes when solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9 include forgetting to consider the charge distribution on the inner and outer surfaces of the shell, not applying the correct boundary conditions, and making calculation errors. It is important to double check all steps and calculations to avoid these mistakes.

5. Are there any helpful tips for solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9?

One helpful tip for solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9 is to break the problem down into smaller, more manageable parts. This can make the problem less daunting and easier to solve. It is also important to carefully label all known and unknown variables and to use the appropriate equations and concepts for each part of the problem.

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