Question

1)If, for a given conductor, the local surface charge density is sigma, what is the direction and magnitude of the electric field in that region? 2)What’s the value of the electric field inside a conductor and why? 3)Where is the excess stationary electric charge located for a conductor and why? 4)What is a Gaussian surface? 5)If you increase/decrease the area of a Gaussian surface, how does the net flux through it changes?

Answer 1

1)The magnitude of the electric field in the region of a charged conductor is given by. The direction of

is at right angles to the surface pointing away from the surface if the charge is positive. This can be found by applying Gauss's law to a hypothetical "pill box" of cross section A as a Gaussian surface.

2)The value of the electric field inside the conductor is zero as all the charge on a conductor settles on its surface so that there is no charge inside the conductor. Therefore by applying Gauss's law to a surface just inside the surface of the conductor we obtain the above result.

3)As already pointed out all the excess stationary charge on a conductor settles on its surface as when electrostatic equilibrium is reached the electric fields inside the conductor are zero. Thus from Gauss's law the result follows.

4)A Gaussian surface is a hypothetical surface constructed in space which may or may not enclose any charge which is drawn to determine the net flux leaving or entering it and thereby relating this net flux to the magnitude of the charge it encloses.This relation is Gauss's law which is given as.

5)The increase or decrease of the area of a Gaussian surface does not change the net flux through it as by Gauss's law it is related only to the charge enclosed by the Gaussian surface and not on the dimensions of the surface.