# Why is the electric field inside a conductor zero?

#### Timebomb3750

1. Homework Statement
Why is the electric field, in static equilibrium, equal to zero.

3. The Attempt at a Solution

The only way I can see why is to picture that there was an electric field inside a conductor. The field would cause the electrons to move freely inside the conductor. This movement of electrons would cancel out the electric field.

That's my two cents. I'm sure I could expand on this more, but I'm confused because I'm having a really hard time trying to picture this in my head.

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#### HallsofIvy

Homework Helper
You can also show this the same way you show that the gravitational force inside a sphere is 0. Given a point, P, inside the sphere, take a small section of surface area on the surface of the sphere and draw a line from every point in that section through P to the other side of the sphere. Note that the area will be directly proportional to the square of the distance from P and since the force is inversely proportional to the square of the distance, the force from the two sections cancel.

#### SammyS

Staff Emeritus
Homework Helper
Gold Member
1. Homework Statement
Why is the electric field, in static equilibrium, equal to zero.

3. The Attempt at a Solution

The only way I can see why is to picture that there was an electric field inside a conductor. The field would cause the electrons to move freely inside the conductor. This movement of electrons would cancel out the electric field.

That's my two cents. I'm sure I could expand on this more, but I'm confused because I'm having a really hard time trying to picture this in my head.
Yes, that's the basic idea.

In a conductor charge is (relatively) free to move. If there were an electric field within a conductor, charges would move. They would move in such a way and to such locations so as to cancel that field.

As a result, any excess local charge can only reside on the surface of a conductor under conditions of equilibrium.

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