Electric field strength inside a conductor

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I read on physics.stackexchange that using Gauss Law we can prove that the electric field strength increases as the radius increases inside a metallic conductor.

Later on the same website, I encountered a contradicting statement that claimed that inside a conductor, the charges aren't free to move hence a resultant force can't effect the charges inside, giving an electric field strength of 0. My question is which statement is correct?

The magnetic field inside a conductor carrying current increases linearly with the radius. Maybe that's what you read?

ZapperZ
Staff Emeritus
I read on physics.stackexchange that using Gauss Law we can prove that the electric field strength increases as the radius increases inside a metallic conductor.

Later on the same website, I encountered a contradicting statement that claimed that inside a conductor, the charges aren't free to move hence a resultant force can't effect the charges inside, giving an electric field strength of 0. My question is which statement is correct?

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/gausur.html

Under electrostatic condition, the electric field inside a conductor is zero.

Zz.

ZapperZ
Staff Emeritus
So would you say the second answer on the link I posted above is wrong?

I wouldn't know. I don't pay attention to stuff posted there. You shouldn't either especially when you have a text that says something to the contrary.

Zz.

Okay can you tell me one thing
We are often taught that laws of gravitation are almost similar to laws of charges

I read about a derivation which went on to conclude that for distances smaller than earth radius the Earth's gravitational field strength becomes proportional to the distance from Earth center. What difference is here and the charges that break this symmetry?

The difference is that electric charges are mobile in a conducting sphere, and they will arrange themselves inside the sphere so that the electric field is zero everywhere inside. The particles creating the gravitational pull (i.e. matter) can't move.

Oh okay thank you very much.

ZapperZ
Staff Emeritus
Okay can you tell me one thing
We are often taught that laws of gravitation are almost similar to laws of charges

I read about a derivation which went on to conclude that for distances smaller than earth radius the Earth's gravitational field strength becomes proportional to the distance from Earth center. What difference is here and the charges that break this symmetry?

1. How well do you know Gauss's Law?

2. Have you seen the Gauss's Law-equivalent for gravitational field?

3. What "symmetry"?

4. If the earth is considered to be a sphere of uniform density, this is no different than a spherical charge with uniform charge density. If you answer "Yes" to my Q1, then you should be able to do the same for gravitational field inside the earth.

Zz.

1,2.Well I am senior high school student so I am not very informative on Gauss Law
3. The symmetry I was talking mainly pertains to the Newton's Law of Gravitation and Coulomb's Law for charges. The Force equation seems very similar to each other and in my high school books, when we are studying about one topic often references are given to the other topic, hence the symmetry
4. So I assume for a spherical charge with uniform density, the electric field strength is proportional to the distance from center (for distance smaller than radius). But if the uniform charge density is not given, then electric field strength is 0 everywhere. Correct?

ZapperZ
Staff Emeritus
1,2.Well I am senior high school student so I am not very informative on Gauss Law

You should always, ALWAYS include such information, especially when you're new here, when asking such question. Otherwise, many of us will waste our time in giving you an explanation that you can't comprehend.

3. The symmetry I was talking mainly pertains to the Newton's Law of Gravitation and Coulomb's Law for charges. The Force equation seems very similar to each other and in my high school books, when we are studying about one topic often references are given to the other topic, hence the symmetry
4. So I assume for a spherical charge with uniform density, the electric field strength is proportional to the distance from center (for distance smaller than radius). But if the uniform charge density is not given, then electric field strength is 0 everywhere. Correct?

I have no idea what you just said here. If the charge density is not given, you cannot assume that it is zero.

Please note that we started with you asking about a conductor. A solid, spherical conductor will have zero electric field inside the conductor under static condition. You cannot equate this with the earth. The earth with a constant density is similar to a dielectric sphere having a uniform charge density. This is where you will have gravitational field inside and outside of the earth, and electric field inside and outside of the sphere. Whereas a charged spherical conductor will only have an electric field outside the sphere and zero inside.

Zz.

Faiq
It should be noted that this result holds just as well for a hollow sphere. I remember finding it odd when I learned it the first time, but when you do the math, it comes out that way.

ZapperZ
Staff Emeritus
It should be noted that this result holds just as well for a hollow sphere. I remember finding it odd when I learned it the first time, but when you do the math, it comes out that way.

I'm trying not to include that because the OP seems to want to equate this with the gravitational field of the earth. And since we don't have a "hollow earth".........

Zz.

You should always, ALWAYS include such information, especially when you're new here, when asking such question. Otherwise, many of us will waste our time in giving you an explanation that you can't comprehend.

I have no idea what you just said here. If the charge density is not given, you cannot assume that it is zero.

Please note that we started with you asking about a conductor. A solid, spherical conductor will have zero electric field inside the conductor under static condition. You cannot equate this with the earth. The earth with a constant density is similar to a dielectric sphere having a uniform charge density. This is where you will have gravitational field inside and outside of the earth, and electric field inside and outside of the sphere. Whereas a charged spherical conductor will only have an electric field outside the sphere and zero inside.

Zz.
I completely understand what you said. Thank you for such a thorough explanation. Can you please provide me some differences of dielectric charged sphere and a solid spherical conductor?

It's the exact difference we mentioned. In a conductor the charges can move, in a dielectric they can't. That's why the former has zero field inside, the latter doesn't.

Faiq
It's the exact difference we mentioned. In a conductor the charges can move, in a dielectric they can't. That's why the former has zero field inside, the latter doesn't.
Precisely, what does the dielectric does that prevent the charges from moving? All I learned about dielectric was they are a medium with a permittivity constant >1

For that I have to refer you to the Wikipedia article on dielectric materials:

https://en.wikipedia.org/wiki/Dielectric

Short answer: Dielectrics are insulators. In insulators, charges don't move (don't move *much*, to be exact. They move a tiny bit, that's what makes them dielectric).

Faiq
jtbell
Mentor
So would you say the second answer on the link I posted above is wrong?
The second answer describes a non-conducting sphere with a uniform charge distribution, which is completely different from the situation presented in the question.

For that I have to refer you to the Wikipedia article on dielectric materials:

https://en.wikipedia.org/wiki/Dielectric

Short answer: Dielectrics are insulators. In insulators, charges don't move (don't move *much*, to be exact. They move a tiny bit, that's what makes them dielectric).
Understood. Thank you for helping

If there is an electric field inside a conductor then charges will move. In a static situation, where charges are not moving, the electric field is zero (otherwise charges would be moving). It's important to state whether the situation is static or not before making a statement about the electric field inside the conductor.