Summary of Mar. 8, 2007


	Coulomb's Law	Mar. 7, 2007

+ Electric field effects: capacitance in devices, field generated by charges (relation to Antenna).

+ Full form of Maxwell's eqns for electric field
[equation] ;

+ Maxwell's eqn for static (DC or low freq) electric field
[equation] ; ; Important!

+ Formal definition of [equation] ; electric force, charge, e.g. electron

+ PROBLEM: Find [equation] for given source(s)? 3 ways

+ 1st method: Coulomb's Law (Sect 3.3)
Electric field intensity of a system with N point charges
[equation]
-- position vector of the observation point p
-- position vector of a source point with charge
permittivity, in free space
Example 3.1: Coulomb's law for a system of point charges
______________________________________

HW #13 (no late homework)	Due 3/14/07

1. A 30 MHz plane wave with [equation]

exists in region [equation]

having

. At

, the wave encounters free space. Determine (a) the polarization of the wave, (b) the phase constant [equation]

, (c)

and

.
2. The plane wave [equation]

V/m in a lossless medium ( [equation]

) encounters a lossy medium ( [equation]

) normal to the x-axis at x=0. Find (a) [equation]

, (b) reflected fields [equation]

and

and (c) transmitted fields [equation]

and

.
Extra-credit:
3. A lossless transmission line operating at 4.5 GHz has [equation]

and

. Calculate (a) the phase constant [equation]

, (b) the phase velocity and (c) if the same line is connected to (terminated in) a load with [equation]

. Find

.
4. A LED is connected to a fiber which has attenuation coefficient [equation]

and is 0.4km long. LED Light is launched from air into one end of the fiber and exits at the other end. The objective of this problem is to find the fraction of power reaching the other end in air. Find (a) the R and T for air to fiber interface, (b) the R and T for fiber to air interface and (c) fraction of power transmitted with the attenuation and reflections in (a) and (b) accounted for. Assume [equation]

and

for the fiber. (Note: You need [equation]

which determined transmitted electric field. Notice the relation between [equation]

and

)

Discussion in uwm.course.ee361