| 1. | Consider two long coils that are wound concentrically on a straight
cylindrical core of radius 
and permeability μ. One of the coils extends a distance 
within the other as the following figure. The two coils have Na
and Nb turns per meter, respectively.Assume that the coils
are thin and long,their diameters are approximately equal and that the
currents Iaand Ibflow in the same direction. Please
find (a) the mutual inductance; (b) Is the force between the two coils
attractive or repulsive? Please find the magnitude of the force. (25%)
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| 2. | The standing wave ratio on a lossless 50 Ω transmission line terminated in an unknown load impedance is found to be 3.0. The distance between successive voltage minima is 20 cm,and the first minimum is located at 5 cm from the load. Determine (a) the reflection coefficient Γ, and (b) the load impedance ZL. (c) Find the equivalent length and terminating resistance of a line such that the input impedance is equal to ZL. (25%) |
| 3. | A uniform plane wave with E=axEx propagates in lossless simple medium (εr=9, μr=1, σ=0) in the +z-direction. Assume that Ex is sinusoidal with a frequency 100 (MHz) and has a maximum value of +10-4 (V/cm) at t=0 and z=1/8 (m). (1) Write the instantaneous expression for E for any t and z. (b) Write the instantaneous expression for H. (c) Determine the locations where Ex is a positive maximum when t=10-8 (s) .(25%) |
| 4. | Consider a uniform sphere of charge of radius R0 and volume charge density ρ. (a) Find the energy required to assemble such a sphere. (b) Determine the electrical field caused by the sphere for 0≦r≦R0 and r≧R0. (c) Please draw the electrical field intensity versus distance r. (25%) |