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Electric Field in Conductors


"It is safe to sit inside the high voltage terminal of a million-volt van de graff generator, without worrying about getting a shock".
- Richard Feynman, The Feynman Lectures on Physics, Vol 2.

The above statement by Feynman shows the interesting beavior of conductors in an electric field. The van de graff generator has a metallic sphere at a very high potential, but the field inside it is zero, so that there is not potential difference between any two points inside the sphere, and hence one would experience no electric shock inside it. This is an example of shielding of electric field by conductors.

Conductor in a static electric field.

Let us first see a basic example of the way conductors behave in an electric field. Assume that there is a metallic conducting block placed in a static electric field (that is, the field is not changing with time). There are a lot of free electrons inside a conductor, which are randomly distributed throughout the bulk of the conductor in the case of no applied electric field. Now when the electric field is applied, the electrons feel a force in the direction opposite to the direction of the field, since they are negatively charged, and hence move to the left surface of the conductor as shown in the figure. This aggregating of electrons to the left surface causes a net positive charge on the right surface.

conductor in electric field

These surface charges would produce an electric field of their own from the right to the left, in a direction opposite to the applied electric field. This transfer of electrons would go on until the field due to these surface charges exactly cancels the applied electric field inside the conductor, since after that, charges inside the conductor do not feel any force.

Thus, because of the presence of free to move charges, the electric field has been cancelled inside the metal. Note again that this true only in case of a static electric field, i.e. electric field that is not changing with time.

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