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 / (20 ) x Ex - d / 2