# Point Charge in an uncharged spherical conductor

## Homework Statement

Consider a point charge q > 0 which is surrounded by a hollow metal sphere (uncharged) with inner radius R1 and outer radius R2. Use Gauss Law to determine the electric field E=E(r)er in the following regions:
(i) 0 < r < R1
(ii) R1 < r < R2
(iii) r > R2

∫EdA = Q/ε

## The Attempt at a Solution

(i) I believe the answer would be 0 because the electric field inside of an enclosed conductor is always zero
(ii) This is where my troubles really lie, don't know what to do here
(iii) I think that the electric field would be equatable to that of one where the point charge didn't exist outside the conductor as long as r is great enough, and i can solve for this

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Consider a point charge q > 0 which is surrounded by a hollow metal sphere (uncharged) with inner radius R1 and outer radius R2. Use Gauss Law to determine the electric field E=E(r)er in the following regions:
(i) 0 < r < R1
(ii) R1 < r < R2
(iii) r > R2

∫EdA = Q/ε

## The Attempt at a Solution

(i) I believe the answer would be 0 because the electric field inside of an enclosed conductor is always zero
(ii) This is where my troubles really lie, don't know what to do here
(iii) I think that the electric field would be equatable to that of one where the point charge didn't exist outside the conductor as long as r is great enough, and i can solve for this
What is the precise location of the charge in the hollow of the sphere?
Is it at the center of the hollow?
Is the center of the hollow coincident with the center of the sphere?​

For items (i) & (ii):
The electric field in the conducting material itself is zero. (This is useful for (ii) but not for (i). )
Nothing says that the electric field must be zero In the hollow of a conductor. Gauss's Law confirms this.​

rude man
Homework Helper
Gold Member

## Homework Statement

Consider a point charge q > 0 which is surrounded by a hollow metal sphere (uncharged) with inner radius R1 and outer radius R2. Use Gauss Law to determine the electric field E=E(r)er in the following regions:
(i) 0 < r < R1
(ii) R1 < r < R2
(iii) r > R2

∫EdA = Q/ε

## The Attempt at a Solution

(i) I believe the answer would be 0 because the electric field inside of an enclosed conductor is always zero
Not if there is charge inside it!

(ii) This is where my troubles really lie, don't know what to do here
Can there be an E field in a conductor?

(iii) I think that the electric field would be equatable to that of one where the point charge didn't exist outside the conductor as long as r is great enough, and i can solve for this
I don't understand this statement.

yes everything is concentric, and I'm starting to see my erroneous thoughts.

(i) would just be the field as if no conductor was present yes? because I am checking the field at which it hasn't reached the conductor

(ii) would be zero because it is inside of the conductor which means the net electric field is zero

(iii) i am now not sure on, but think that it may be the same answer as (i) because the charge (lets say positive) in the conductor would pull all the electrons to the inside, leaving the outside of the conductor positively charged just like it would be before. Is this correct in theory?

SammyS
Staff Emeritus
Homework Helper
Gold Member
yes everything is concentric, and I'm starting to see my erroneous thoughts.

(i) would just be the field as if no conductor was present yes? because I am checking the field at which it hasn't reached the conductor

(ii) would be zero because it is inside of the conductor which means the net electric field is zero

(iii) i am now not sure on, but think that it may be the same answer as (i) because the charge (lets say positive) in the conductor would pull all the electrons to the inside, leaving the outside of the conductor positively charged just like it would be before. Is this correct in theory?
Pretty much correct.

In (iii), it's not true that all the electrons are pulled to the inside. Gauss's Law tells us that just enough electrons are pulled to the inside so that the flux in the conducting material is zero. ...