Electric field lines from a metal shell and sphere

[Sho Kano]

Homework Statement

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?

Homework Equations

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.

 

[haruspex]

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.

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.

 

[Sho Kano]

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.

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

 

[haruspex]

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

Yes.