3 concentric conducting spheres, the outer one connected to ground

  • #1
Sokolov
14
1
Homework Statement
Three concentric conductor spheres, the outer of them connected to ground, have electrical charges[itex]Q_A[/itex], [itex]Q_B[/itex] and [itex]Q_C[/itex], and radii[itex]R_1[/itex], [itex]R_2[/itex], [itex]R_3[/itex], [itex]R_4[/itex] and[itex]R_5[/itex], from the inner to the outer. Find the induced charges and the equations of the electric field and the potential of the system.
Relevant Equations
[tex] \oint \vec E\cdot d\vec S =\frac{q}{\epsilon_0}[/tex]
Esferas.png

What would the fact that the fifth surface is connected to the ground imply: that [itex]V(r=R_5)=0[/itex] or that [itex]\sigma _5=0[/itex]?
 
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  • #2
Hello Sokolov, :welcome: !

Ground is considered ##V=0##.
Perhaps not extremely interesting for part two, since ##E## is a derivative.
 
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  • #3
Sokolov said:
Homework Statement:: Three concentric conductor spheres, the outer of them connected to ground, have electrical charges[itex]Q_A[/itex], [itex]Q_B[/itex] and [itex]Q_C[/itex], and radii[itex]R_1[/itex], [itex]R_2[/itex], [itex]R_3[/itex], [itex]R_4[/itex] and[itex]R_5[/itex], from the inner to the outer. Find the induced charges and the equations of the electric field and the potential of the system.
Relevant Equations:: [tex] \oint \vec E\cdot d\vec S =\frac{q}{\epsilon_0}[/tex]

View attachment 258000
What would the fact that the fifth surface is connected to the ground imply: that [itex]V(r=R_5)=0[/itex] or that [itex]\sigma _5=0[/itex]?
Couple of hints to add to BvU's:
1. what can you say about ##\sigma_2 ## vs. ##\sigma_1 ##? Etc?
2. What must be the field outside R5? What does that imply for ## \sigma_5 ## assuming you've worked out the other sigmas?

P.S. ## \sigma_i ## means charge density on surface i.
 
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  • #4
BvU said:
Hello Sokolov, :welcome: !

Ground is considered ##V=0##.
Perhaps not extremely interesting for part two, since ##E## is a derivative.

Hi BvU, thanks for the answer! It was just what I needed to know in order to be able to solve the problem.
 
  • #5
rude man said:
Couple of hints to add to BvU's:
1. what can you say about ##\sigma_2 ## vs. ##\sigma_1 ##? Etc?
2. What must be the field outside R5? What does that imply for ## \sigma_5 ## assuming you've worked out the other sigmas?

P.S. ## \sigma_i ## means charge density on surface i.

Thanks rude man! With your hints and BvU's answer I think that I have been able to solve the problem correctly :) .
 
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