Grounded sphere in Electric field

[lswtech]

Homework Statement

Homework Equations

Electrostatic induction

The Attempt at a Solution

I thought that at steady states, the potential over a conductor should remain constant and holds 0V potential as it is grounded and hence the option (1) should be correct. However, the answer is B.

I have searched through the internet and got a site http://www.esdjournal.com/techpapr/eosesd/failures/induct.htm . The author claims it is a general misconception to "think that a conductor is always at the same potential at all surface locations". Shouldn't there be no charge flowing in equilibrium and hence the entire metal surface shares the same potential? Thanks in advance.

 

[cupid.callin]

field won't be 0
it will be from P to R (unless we are talking about a point inside sphere R)
thats why i think question is incomplete ... we don't know weather question is talking about a point on surface or interior of R

 

[gneill]

Charges on a conductor will rearrange themselves in response to an external electric field in such a way as to make the net internal electric field zero. When that happens there is a static equilibrium (Ha! a pun) between the field produced by the external field and that produced by the rearranged charges. This is a form of induction, where an induced potential difference is created on a conductor due to the presence of an external field.

In the case of the small grounded sphere, there's actually a source for charges to come and join in the fun by drawing them up through the grounding wire. The surface of the small sphere nearest the larger charged sphere will gain a concentration of negative charges, and a net charge will appear on the small sphere (so an electric field will be produced, also).

 

[lswtech]

In the case of the small grounded sphere, there's actually a source for charges to come and join in the fun by drawing them up through the grounding wire. The surface of the small sphere nearest the larger charged sphere will gain a concentration of negative charges, and a net charge will appear on the small sphere (so an electric field will be produced, also).

But won't the "electric field produced" cancel off the external field and make the net field 0, at equilibrium?

 

[gneill]

But won't the "electric field produced" cancel off the external field and make the net field 0, at equilibrium?

Well, the net field will be zero inside the small sphere, if that's what you mean. Outside the sphere you'll have the two fields doing what fields do in free space.

 

[lswtech]

Well, the net field will be zero inside the small sphere, if that's what you mean. Outside the sphere you'll have the two fields doing what fields do in free space.

Then will the Potential in R be 0V too?

 

[gneill]

Then will the Potential in R be 0V too?

What does potential mean when there is no field?

 

[lswtech]

What does potential mean when there is no field?

I thought there could be potential due to surrounding objects even if the sphere carries no field interiorly. Then in this case, the Option (1) is valid as far as it is dealing with the "field and potential inside R"?

 

[gneill]

The potential that shows up on the sphere R shows up on its surface. To the outside world it will have an electric field and a potential. Inside the sphere there is no field.

 

[cupid.callin]

What does potential mean when there is no field?

Think of E = -dV/dl

if E is 0 then V is some constant value

 

[lswtech]

Think of E = -dV/dl

if E is 0 then V is some constant value

So can I conclude that: for any grounded metal object, at equilibrium, the field inside is 0 as well as its potential ,over the surface and at everywhere eise, is 0?

I believed in this until I came across an article: http://www.esdjournal.com/techpapr/eosesd/failures/induct.htm It seems to outline something different from what I stated above, and got confused about it.

 

[cupid.callin]

So can I conclude that: for any grounded metal object, at equilibrium, the field inside is 0 as well as its potential ,over the surface and at everywhere eise, is 0?

I believed in this until I came across an article: http://www.esdjournal.com/techpapr/eosesd/failures/induct.htm It seems to outline something different from what I stated above, and got confused about it.

For any conducting object field inside is 0
and potential is 0 when the object is grounded