why is E-field inside a conductor zero? Please look at this image from the text book

yellowbus

The image below is from giancoli. There is clearly an electric field inside the conductor, going from the + charge on the outside surface of the wheel to the - charge on the inside surface of the wheel. There is an electric field inside this conductor because if I drop a + test charge in the middle of the wheel (between the outer and inner surfaces), the electric field would take the test charge to the outside surface of the wheel. Is this image just misleading?

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Pengwuino

You are forgetting that you are dealing with electrostatics. Electrostatics concerns the study of electric fields when all the charges are static. If you placed a test charge inside the conductor, it would not move as there is no electric field. If you dump a real charge on the inside, it would spread out to the edges until the system came into equilibrium and returned to a static situation. You would again find yourself with no electric field on the inside.

yellowbus

okay, I drew the E-field vectors in blue arrows going from the positive charges to the negative charges along the surface of the wheel. Are you saying this doesn't exist?

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Born2bwire

Yes, there is no electric field inside the conductor. The charges in a conductor are free to move about. So anytime that you have an applied electric field, the charges will move throughout the conductor so long as a net electric field inside the conductor exists. However, the charges move in such a way that they create a second electric field that opposes the applied field. Thus, eventually the charges will move and configure themselves in such a way that there no longer exists any net field inside the conductor. Pengwuino stated that you need to keep in mind that this is electrostatics, so we can assume that the field was applied an infinite amount of time ago. So regardless of how slow the charges take to configure themselves (which in actuality is rather quick), they will eventually arrange themselves to expel the applied field.

In your example, take note of the directions of the electric fields. The applied field points radially outward and induces a negative charge on the inside wall and a positive charge on the outside wall. Inside the conductor, these negative charges create an electric field that will point radially inward. The positive charges likewise create an electric field that points inward. So you can see that the induced charges create fields that oppose the applied field.