Notes 11 ECE 2317 Applied Electricity and Magnetism Prof. D. Wilton ECE Dept. Gauss Notes 11 Notes prepared by the EM group, University of Houston.

Example r h Assume S l = l0 [C/m] infinite uniform line charge z y z S l = l0 [C/m] h r Find the electric field everywhere Assume infinite uniform line charge

Example (cont.) h St Sb Sc  r

Example (cont.) Hence So

Example S h a  r Assume v = 3 2 [C/m3] ,  < a y z S h a  r Find the electric field everywhere Assume v = 3 2 [C/m3] ,  < a non-uniform infinite cylinder of volume charge density

Example (cont.) (a)  < a  S r h

Example (cont.) Hence So

Example (cont.) (b)  > a S  h r

Example When Gauss’s Law is not useful: But (1) (2) y z l0 -h When Gauss’s Law is not useful: But (1) (2) (the charge density is not uniform!) (3) E has more than one component

Example s = s0 [C/m2] r A S Find the electric field everywhere z Assume S A r

Example (cont.) S A r Assume

Example (cont.) S A r so ( Generally, Ez is continuous except on either side of a surface charge)

Example slab of uniform charge r x Find the electric field everywhere Assume (since Ex(x) is a continuous function)

Example (cont.) A (a) x > d / 2 x x r S d

Example (cont.) Q Q d v0 seff A A Note: If we define then (sheet formula) Q Q d v0 seff A A

Example (cont.) (b) 0 < x < d / 2 x r x = x d S y x = 0

Example (cont.) x Summary d y d / 2 v0 d / (20 ) x Ex - d / 2