Question

What is the magnitude of the force per unit area between two infinite, uniformly charged plates with a surface charge density of +4.20

Answer 1

Consider an infinite plane which carries the uniform charge per unit area . Suppose that the plane coincides with the - plane (i.e., the plane which satisfies ). By symmetry, we expect the electric field on either side of the plane to be a function of only, to be directed normal to the plane, and to point away from/towards the plane depending on whether is positive/negative.

Figure : The electric field generated by a uniformly charged plane.

Let us draw a cylindrical gaussian surface, whose axis is normal to the plane, and which is cut in half by the plane--see Fig. Let the cylinder run from to , and let its cross-sectional area be . According to Gauss' law,

therefore, so force F= Charge (q)* Electric Field (E). force per unit area (F/A)= q*E/A. F/A= (q/A)*E. F/A= *E -------------------------F/A=(^2)/(2*E0).------------------- For two plates of oppsite sign charge density, force is equal in magnitude but different in direction. Ans A) F/A=(4.20