3 concentric conducting spheres, the outer one connected to ground

[Sokolov]

Homework Statement

Three concentric conductor spheres, the outer of them connected to ground, have electrical charges$Q_A$, $Q_B$ and $Q_C$, and radii$R_1$, $R_2$, $R_3$, $R_4$ and$R_5$, 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

$$\oint \vec E\cdot d\vec S =\frac{q}{\epsilon_0}$$

What would the fact that the fifth surface is connected to the ground imply: that V(r=R_5)=0 or that \sigma _5=0?

 

[BvU]

Hello Sokolov, !

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

 

[rude man]

Homework Statement:: Three concentric conductor spheres, the outer of them connected to ground, have electrical chargesQ_A, Q_B and Q_C, and radiiR_1, R_2, R_3, R_4 andR_5, 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:: \oint \vec E\cdot d\vec S =\frac{q}{\epsilon_0}

View attachment 258000
What would the fact that the fifth surface is connected to the ground imply: that V(r=R_5)=0 or that \sigma _5=0?

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.

 

[Sokolov]

Hello Sokolov, !

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.

 

[Sokolov]

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 :) .