1) A charged particle with charge +q sits at position A as shown below.

a. If the particle at position B has no charge, what is the force on the particle at A?

b. What charge should be placed on the particle at position B such that the force on the particle at A is exactly zero.

2) A sphere of radius 2 meters (re) has a uniform charge density of 100 nC/m³ throughout its volume except for a hollow center in which no charge resides. The radius of the hollow portion is 0.5 meters, rA. The material inside the sphere has a relative dielectric constant Er of 10. Outside the sphere is free space.

a. find D for r < rA
b. find D for rA < r < rB
c. find D for r > rtt
d. sketch a plot of IDS vs r out to r = 2re
e. Show that the integral ∫ D•dS over the surface of the sphere gives a result equal to the total charge within the sphere (Gauss's Law).

3) Given a metal rod placed along 2 conducting wires connected by a 20 ohm resistor initially forming a 1 square meter area as shown, sketch the voltage reading versus time given the plot of position versus time. Be sure to carefully determine the polarity of the measurement and also show the magnitude of Vin order to get full credit. The B field is 10 Tesla, directed out of the page.

4) A long cylindrical conductor of radius a = 10 mm oriented along the z-axis carries a current density according to J = 5ρ az (where p is the cylindrical radius).

a. Find the total current, I.

Using Ampere's Law:

b. What is H for 0 < ρ < a? (include direction)

c. What is H for ρ > a?

d. find V x H for both b) and c). Do your answers support Stoke's Law?

5) A 50 ohm transmission line has a resistive load of 40 ohms at its far end. Using a Smith chart, give the sign of and estimate the magnitude and location of the reactive series element necessary to eliminate reflections in the system. (express the location in terms of wavelengths from the load. Label your line segments and points on your Smith chart as appropriate.)

6) In a dielectric material (sigma = 0, tri=3, uri=1) a 100 MHz propagating plane wave's E field in phasor notation is given by E = 200 e-J(47V3)z az [V/m].

Determine the following:

a) The velocity of propagation.

b) The wavelength.

c) The wave impedance

d) The magnitude and orientation of the H component of the wave.

e) The wave propagates into another material and its velocity is seen to drop by a factor of 4. What is the relative permittivity cr2 of material 2?