University physics - conducting concentric spheres

[SunSmellsLoud]

Homework Statement

Two hollow conducting spheres are connected electrically, and are charged to a potential V. The connection is then removed and the outside sphere is grounded, find the charge and potential of the inner sphere after the grounding.

2. The attempt at a solution
I'm not looking for a full solution as that would be (in my eyes) cheating, but my question is whether or not there WILL be a charge on the inner sphere. If all the charge resides on the surface of a conductor, and the spheres are electrically connected, surely all the charge will just reside on the outside of the outer sphere.

Hence, after grounding, wouldn't the charge on both spheres be 0, and no potential between them?

Thanks in advance.

 

[Adithyan]

There will be a charge on the inner sphere and the charge on the outer sphere is NOT zero. It has a finite value.
Different charges are possessed by the spheres at the time when the conducting wire was removed. Now, think why the surface charge density on the outer surface of the outer sphere is not zero when earthed.

Hint: Think in terms of field and potential difference due to the net field. And don't make any mistake while calculating the net field at a point outside the spheres.

 

[SunSmellsLoud]

Okay thanks for the hint, however I've been thinking about this all day, and have consulted with the other people doing the question. We cannot come to a reasonable conclusion at all so any mathematical help would at this point be much appreciated.

 

[Adithyan]

Earthing means to force the potential of the body earthed to zero. And zero potential means, the potential of the body is not altered by the time it brought from infinity to the present position (i.e, at infinity potential=0 and at the point of earthing potential =0). Therefore potential difference is zero leading to zero external field.

Now try equating the net field at point outside the sphere to zero. And mark the charge of the outer sphere as q' and inner charge as q".

 

[HalfLostAndSearching]

Your understanding is correct. Since the two spheres are connected electrically, the charge will distribute itself evenly on the surface of both spheres. After grounding the outer sphere, the charge on both spheres will be zero and there will be no potential difference between them. This is known as the principle of equipotentiality, where all points on a conductor at the same potential are connected by a conductor. Therefore, the charge and potential of the inner sphere after grounding will be zero.