# Electric field lines from a metal shell and sphere

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1. Apr 1, 2016

### Sho Kano

1. The problem statement, all variables and given/known data
A metal sphere of charge +6μC is surrounded by a metal shell of net charge +6μC. Which of the following diagrams represents the electric field lines of the system?

2. Relevant equations

3. The attempt at a solution
The correct answer provided by my teacher is a figure with 12 arrows pointing out of the shell, and 6 arrows pointing out of the inner sphere.

Can you guys explain to me physically and in detail why this is the case? My guess is that since the net charge of the system is 6+6=12μC, 12 arrows would be pointing out in total.

2. Apr 1, 2016

### haruspex

That is correct. If you want a more detailed view, consider how the charges on the shell are distributed between its inner and outer surfaces.

3. Apr 1, 2016

### Sho Kano

Hi haruspex,
I'm guessing that the inner +6μC would induce a -6μC on the inner surface of the outer shell. Thus the total charge Q is:
Q = 6 = -6 + q_outer
q_outer = +12μC

4. Apr 1, 2016

Yes.