Chapter 23, Problem 69EAP

a. An infinitely long sheet of charge of width L lies in the xy-plane between $x=-L/2$ and $x=L/2$ . The surface charge density is $\eta$ . Derive an expression for the electric field E along the x-axis for points outside the sheet $(x>L/2)$ .

b. Verify that your expression has the expected behavior if $x\gg L$ Hint: In $(1+u)\approx u$ if $u\ll 1$ .

c. Draw a graph of field strength E versus x for $x>L/2$ .