Why is the electric field inside a conductor zero?

In summary, the electric field is equal to zero in static equilibrium because charges within a conductor will move in a way that cancels out the field, leaving any excess charge to reside on the surface of the conductor. This can be demonstrated by comparing it to the gravitational force inside a sphere, where the force from different sections of the surface cancel out.
  • #1
Timebomb3750
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0

Homework Statement


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

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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  • #2
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.
 
  • #3
Timebomb3750 said:

Homework Statement


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

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.
 

1. Why is the electric field inside a conductor zero?

The electric field inside a conductor is zero because the free charges within the conductor redistribute themselves until there is no net electric field inside. This is known as electrostatic equilibrium.

2. How does the redistribution of charges lead to a zero electric field inside a conductor?

When an external electric field is applied to a conductor, the free charges within the conductor are attracted to the opposite side of the field and repelled from the same side. This results in a separation of charge that creates an electric field inside the conductor. However, as the charges continue to move, they eventually reach a state of equilibrium where the electric field inside the conductor becomes zero.

3. Is the electric field inside a conductor always zero?

No, the electric field inside a conductor is only zero when the conductor is in electrostatic equilibrium. If there is a changing external electric field, the charges within the conductor will continue to redistribute themselves and the electric field inside may not be zero.

4. How does the shape of a conductor affect the electric field inside?

The shape of a conductor does not affect the electric field inside as long as the conductor is in electrostatic equilibrium. This is because the charges will always redistribute themselves to cancel out any external electric field, regardless of the shape of the conductor.

5. What happens to the electric field inside a conductor if the conductor is not in electrostatic equilibrium?

If the conductor is not in electrostatic equilibrium, the electric field inside may not be zero. The charges within the conductor will continue to move in response to the external electric field, resulting in a non-zero electric field inside the conductor.

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