Solved: Griffiths Ex. 3.6 - Is There Charge Inside the Sphere?

In summary, Griffiths says that there is no charge inside the sphere, but that assumption is necessary in order to use the solutions to Laplace's equations.
  • #1
ehrenfest
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[SOLVED] Griffiths Example 3.6

Homework Statement


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

In Example 3.6, we must assume that there is no charge inside the sphere even though it does not explicitly state that? Or is that what "hollow" means?


Homework Equations





The Attempt at a Solution

 
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  • #2
No hollow simply means in this case the potential is only in tin shell on the surface rather then being throughout which would make [tex] A_l [/tex] obsolete. As long as it not specifically stated that there is net charge or not we assume there isn't. All the charges are positioned homogeneously throughout
 
  • #3
So you are saying that we do assume there is no charge inside the sphere, correct?

He explicitly says that the charge is on the surface? What does "hollow" add to the problem?
 
  • #4
No, what happens is that there is no NET charge. There is still charge around, but the overall contribution is such that the charges chancel each other out. look at example 3.8 and see how the electric field causes the charges to accumulated and "charge" even though it is an "uncharged" metal sphere.

Hollow is simply saying that there is a potential within the thing, else there would not be from what i understand.
 
  • #5
But Laplace's equation does not apply unless there not only no net charge but exactly 0 charge density everywhere inside the sphere. And if Laplace's equation does not apply, neither do the solutions (eqn 3.65) that he uses.
 
  • #6
Read Section 3.1.1 and look at the example 3.3, 3.4, 3.5. It states that we don't need a charge to have a potential. There is no net charge. LaPlace is equal to 0. The same is true for this section if you look at Eqn 3.53 from which Eqn 3.65 are derived
 
  • #7
I don't think you understand my question.

In Example 3.7, Griffiths says "assuming there is no charge there". Why does he not say that in Example 3.6? I contend that he made a mistake and that he should have said it in Example 3.6. If that assumption is not made, then everything in Example 3.6 makes no sense.

Please confirm this.
 
  • #8
He means no free charge OUTSIDE the sphere, else it would influence the result, as the boundary conditions would change. With only the sphere as a source of potential the normal boundary conditions can be used
 
  • #9
I still think you don't understand my question.

I am asking about the assumptions we are making in Example 3.6. In Example 3.7, Griffiths says explicitly that there is no charge anywhere outside of the sphere. In Example 3.6, he does not say that there is no charge inside the sphere. But that is an assumption that is necessary in order to use the solutions to Laplace's equations.
Someone please confirm this.
 
  • #10
Yes there is no charge inside, cause else he would state it. The problem of the charge inside comes later in a different version, dipole in dielectric
 
  • #11
OK. That's all. Thanks.
 

Related to Solved: Griffiths Ex. 3.6 - Is There Charge Inside the Sphere?

1. What is Griffiths Ex. 3.6 and why is it important?

Griffiths Ex. 3.6 refers to Exercise 3.6 in the textbook "Introduction to Electrodynamics" by David J. Griffiths. This exercise deals with the concept of charge distribution inside a conducting sphere and is important because it helps us understand the behavior of electric fields and charges in different scenarios.

2. Is there charge inside the sphere in Griffiths Ex. 3.6?

No, there is no charge inside the conducting sphere in Griffiths Ex. 3.6. This is because, in a conductor, charges are free to move and redistribute themselves in order to cancel out any external electric field. Therefore, the electric field inside a conductor is always zero.

3. How does the charge distribution inside a conducting sphere affect the electric field outside the sphere in Griffiths Ex. 3.6?

The charge distribution inside a conducting sphere affects the electric field outside the sphere by creating an equivalent charge distribution on the surface of the sphere. This surface charge distribution produces an electric field outside the sphere, which is the same as that of a point charge located at the center of the sphere.

4. Can the charge distribution inside a conducting sphere in Griffiths Ex. 3.6 be changed?

Yes, the charge distribution inside a conducting sphere can be changed by introducing a non-uniform charge distribution on the surface of the sphere. This can be done by placing different objects or charges on the surface of the sphere, which will redistribute the charges inside the sphere accordingly.

5. How is Griffiths Ex. 3.6 relevant to real-life applications?

Griffiths Ex. 3.6 is relevant to many real-life applications, such as the behavior of electric fields and charges in conductors, capacitors, and other electrical devices. Understanding the principles behind charge distribution inside a conducting sphere can also help in designing efficient and effective electrical systems.

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