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Explain Gauss' Law?

7 years ago

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Conductors in Electric Fields




A large number of electrons in a conductor are free to move. The so called free electrons are the cause of the different behavior of conductors and insulators in an external electric filed. The free electrons in a conductor will move under the influence of the external electric field (in a direction opposite to the direction of the electric field). The movement of the free electrons will produce an excess of electrons (negative charge) on one side of the conductor, leaving a deficit of electrons (positive charge) on the other side. This charge distribution will also produce an electric field and the actual electric field inside the conductor can be found by superposition of the external electric field and the induced electric field, produced by the induced charge distribution. When static equilibrium is reached, the net electric field inside the conductor is exactly zero.


This implies that the charge density inside the conductor is zero. If the electric field inside the conductor would not be exactly zero the free electrons would continue to move and the charge distribution would not be in static equilibrium. The electric field on the surface of the conductor is perpendicular to its surface. If this would not be the case, the free electrons would move along the surface, and the charge distribution would not be in equilibrium. The redistribution of the free electrons in the conductor under the influence of an external electric field, and the cancellation of the external electric field inside the conductor is being used to shield sensitive instruments from external electric fields.

The strength of the electric field on the surface of a conductor can be found by applying Gauss' law. The electric flux through the surface shown in Figure is given by


 



 

where A is the area of the top of the surface shown in Figure The flux through the bottom of the surface shown in Figure is zero since the electric field inside a conductor is equal to zero. Note that eq. is only valid close to the conductor where the electric field is perpendicular to the surface. The charge enclosed by the surface shown in Figure is equal to

 






Electric field of conductor.

 

where [sigma] is the surface charge density of the conductor. is correct if the charge density [sigma] does not vary significantly over the area A (this condition can always be met by reducing the size of the surface being considered). Applying Gauss' law we obtain

 



 


Thus, the electric filed at the surface of the conductor is given by



 

7 years ago

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