Electric field within a conductor with a cavity

[henry3369]

Homework Statement

I'm having trouble understanding my book's explanation of the electric field within a conductor with a cavity.

http://imgur.com/mjHRQoq

Homework Equations

EA = q_enc/ε

The Attempt at a Solution

So I understand the first two pictures, the electric field is 0 because the Gaussian surface does not contain any charges. Then on the third image I am confused when a positive charge is introduced in the cavity of the conductor.

1. Where do the random negative charges come from in the last picture?
2. Why does the electric field have to be zero for all points on the surface? If you look at the picture in the middle (b), the picture shows the charges all on the outside surface. If you introduce a positive charge, q, then q(enclosed) will not be zero and the electric field is not zero anymore. Instead, the book introduces random negative charges just to make q(enclosed) = 0. Couldn't I just randomly introduced negative charges on the interior of the Gaussian surface for an empty cavity then and say that electric field is not zero?

 

[SammyS]

Homework Statement

I'm having trouble understanding my book's explanation of the electric field within a conductor with a cavity.

http://imgur.com/mjHRQoq

Homework Equations

EA = q_enc/ε

The Attempt at a Solution

So I understand the first two pictures, the electric field is 0 because the Gaussian surface does not contain any charges. Then on the third image I am confused when a positive charge is introduced in the cavity of the conductor.

1. Where do the random negative charges come from in the last picture?
2. Why does the electric field have to be zero for all points on the surface? If you look at the picture in the middle (b), the picture shows the charges all on the outside surface. If you introduce a positive charge, q, then q(enclosed) will not be zero and the electric field is not zero anymore. Instead, the book introduces random negative charges just to make q(enclosed) = 0. Couldn't I just randomly introduced negative charges on the interior of the Gaussian surface for an empty cavity then and say that electric field is not zero?

1.Where do the random negative charges come from in the last picture?
It's a conductor. It's made up of billions & billions -- way more than that actually -- of positive & negative charge and in which some of the charge is free to move around. The negative charge is attracted by that appealing positive charge at the center.

Think about this. Maybe the answer to #2. will come to you. Right now #2 is a jumble of thoughts & questions.

 

[henry3369]

1.Where do the random negative charges come from in the last picture?
It's a conductor. It's made up of billions & billions -- way more than that actually -- of positive & negative charge and in which some of the charge is free to move around. The negative charge is attracted by that appealing positive charge at the center.

Think about this. Maybe the answer to #2. will come to you. Right now #2 is a jumble of thoughts & questions.

Ok. So originally I was thinking that the conductor had only positive charges for some reason. So now I understand that the negative charges are there because the charge insert in the cavity attracts them.

So now my book is saying that if the original charge on the conductor was qc, the new charge on the surface is qc+q after q was inserted. If this was the case, the Gaussian surface in (c) wouldn't contain q anymore, so would the situation be similar to (b) again?

 

[Hesch]

Homework Statement

I'm having trouble understanding my book's explanation of the electric field within a conductor with a cavity.

http://imgur.com/mjHRQoq

Homework Equations

EA = q_enc/ε

The Attempt at a Solution

So I understand the first two pictures, the electric field is 0 because the Gaussian surface does not contain any charges. Then on the third image I am confused when a positive charge is introduced in the cavity of the conductor.

1. Where do the random negative charges come from in the last picture?
2. Why does the electric field have to be zero for all points on the surface? If you look at the picture in the middle (b), the picture shows the charges all on the outside surface. If you introduce a positive charge, q, then q(enclosed) will not be zero and the electric field is not zero anymore. Instead, the book introduces random negative charges just to make q(enclosed) = 0. Couldn't I just randomly introduced negative charges on the interior of the Gaussian surface for an empty cavity then and say that electric field is not zero?

You can never have a static electric field within a conducting material. If you ( within 1 ps ) place a charge in the cavity, you will get an electric field through the conducting material outside the cavity, but opposite charged paticles in the conducting material will immediately be attracted as close as possible, until the electric field in the conductor is eliminated. So the negative charges come from the conducting material, and when the material is "drained" of negative charges, a surplus of positive charges will be left on the outer surface of the conductor.

Of course you can have an electric field, for example in a resistor when current is flowing through it, but this is not a static electric field.

 

[SammyS]

Ok. So originally I was thinking that the conductor had only positive charges for some reason. So now I understand that the negative charges are there because the charge insert in the cavity attracts them.

So now my book is saying that if the original charge on the conductor was qc, the new charge on the surface is qc+q after q was inserted. If this was the case, the Gaussian surface in (c) wouldn't contain q anymore, so would the situation be similar to (b) again?

The location of the Gaussian surface in both (b) and (c) is in the conducting material itself. As Hesch points out, there cannot be a static electric field within the conducting material. It turns out that if there is any excess charge (either positive or negative) on a conductor it must reside on the surface of the conductor.

So the electric flux exiting the Gaussian surface is zero, because the electric field is zero everywhere on that surface. Gauss's Law tells you that the net charge enclosed by the surfaces in both (b) and (c) is zero. In other words, in each case the total amount of negative is equal to the total amount of positive charge. In case (c), that means that amount of charge on the inner surface of the cavity must be an equal quantity but opposite sign of the isolated charge inside the cavity.