Spherical Capacitor: Explaining Inner Sphere Grounding

[Molar]

When the inner sphere of a spherical capacitor is grounded and a charge is given to the outer sphere, then it is said that two capacitors are in parallel :
1) outer sphere and the ground and
2) inner sphere and the inner surface of the outer sphere.

My question is about the second one.
Since the inner sphere is grounded, does not it mean that all the induced charge of the inner sphere will be grounded ? Then the second capacitor should also be between the inner surface of the outer sphere and the ground.

Where am I going wrong ?

 

[Charles Link]

The inner sphere will be at zero potential, but it will develop a charge on it. Because the electric field is zero inside the solid part of the outer sphere, the charge contained on the outer surface of the inner sphere must be equal and opposite the charge on the inner surface of the outer sphere. The charge on the outer surface of the outer sphere is not equal and opposite the charge on the inner surface of the outer sphere. The total charge in the problem equals zero so there must be a huge (infinite) surface at ground outside the problem that has a charge equal and opposite that of the charge on the outer surface of the outer sphere. .. editing.. There needs to be a small wire going through a hole in the outer sphere that connects to the inner sphere that connects to the outside (infinite) ground. Then there is also a voltage source between this ground and the surface of the outer sphere.

 

[Molar]

I am probably being dumb here, still can you explain this ?

The total charge in the problem equals zero

How the total charge of the system is zero when Q charge is given to the outer surface of the outer sphere ?

 

[Charles Link]

I am probably being dumb here, still can you explain this ?How the total charge of the system is zero when Q charge is given to the outer surface of the outer sphere ?

The charge comes from the ground which is considered part of the system. The whole system is assumed to start out in a neutral=uncharged condition. A voltage source is connected which causes the charges to shift=parts become positive and parts negative, etc. Essentially the charge flow is all due to electrons, but two things balance here: If the charge on the outer surface of the inner sphere is $-Q_A$, then the charge on the inner surface of the outer sphere is $+Q_A$. If the charge on the outer surface of the outer sphere is $+Q_B$, then the charge on the ground surface (apart from the inner sphere) is $-Q_B$. The ground is connected to the inner sphere, so the total charge there is $-Q_A+-Q_B$. The total charge on the outer sphere is $+Q_A+ +Q_B$. The values for $Q_A$ and $Q_B$ depend on geometry as well as the applied voltage.

 

[Molar]

Ahh..It's much clearer now.
I want to clear another thing. Previously somehow I thought, the outer surface of the inner sphere will have -Q_A charge and hence the inner surface of the inner sphere will have +Q_A charge. This +Q_A charge will go to the ground.

But now I think that was wrong. Initially the inner surface of the inner sphere will have no charge (because no charge can reside inside a conducting surface,but on the surface ) and later -Q_B charge will flow to it from the ground. Am I right now ?

 

[Charles Link]

Ahh..It's much clearer now.
I want to clear another thing. Previously somehow I thought, the outer surface of the inner sphere will have -Q_A charge and hence the inner surface of the inner sphere will have +Q_A charge. This +Q_A charge will go to the ground.

But now I think that was wrong. Initially the inner surface of the inner sphere will have no charge (because no charge can reside inside a conducting surface,but on the surface ) and later -Q_B charge will flow to it from the ground. Am I right now ?

Very Good. I believe you have it correct.

 

[Molar]

Thank you so much for helping me throughout the problem.