Question

a) Use the Gauss Law to find the electric field at point P at distance z from the infinite plane of surface density ?. Make sure to briefly explain all the steps (annotate them briefly, as in class notes). Take particular care (to explain why!) if the flux through certain area is 0. b) Explain in what situation may we find such expression useful.

Answer 1

(a) + 1 T + + + + + + хуу /tdt In figure let us consider a plane sheet of charge density 5. The charge on the sheet is, Q = oA 0 het a Gaussian cylinder Ž across the sheet, as a Gaussian surface, having base. asea A. Totul electric flux across this cylinder is given by - 0= EA tot EA $ = 2EA —— (2), Grauss's theorem, gives, $= e = A —) From (P) $ (3), weget, 2EA = TEM Infinite plane of charge. (b) Hence, electric field at a distance z from sheet is E 2 , which does not depends on distance z. This expression Ece is used to find the electric fields at various point near the infinitely plane sheet of charge. This is also used to find the electric field intensity near the surface of conductor and charged. isolated conducting plate. 24o