(a) Define electric flux. Write its S.I. units.

(b) Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.

(c) How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?     

a) Electric flux is defined as the total number of electric field lines passing through an area normal to them.


SI unit is Nm²/C.

 b) Gauss’s theorem states that the total electric flux through a closed surface is equal to  times the net charge enclosed by the surface. 

 

Consider a uniformly charged infinite plane sheet of charge density  .

Consider a Gaussian surface inside as shown in the figure which is in the form of a cylinder.

On applying Gauss’s law, we have

 

Thus, electric field strength due to an infinite flat sheet of charge is independent of the distance of the point and is directed normally away from the charge.

If the surface charge density s is negative the electric field is directed towards the surface charge.

c) i) Away from the charged sheet.

ii) towards the plane sheet.