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ECE3209-2009-hw4

# ECE3209-2009-hw4 - electric ﬁeld lines and equipotentials...

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ECE 3209 — Electromagnetic Fields University of Virginia Fall 2009 Homework # 4 — Conductors, Polarization, and Dielectrics Due: Friday, October 2 1. Consider two perfectly conducting spheres of radii a and b , respectively, that are connected by a long, thin conducting wire as shown below. Assume the wire does not disturb the field distribution around the spheres, but only serves to keep them at the same potential. If a total charge, q , is placed on this structure, find the charge that resides on each sphere and the ~ E field on the surface of each sphere. (Note: your result should help you explain how a lightning rod works. A lightning rod is a sharp metal rod placed on the top of tall buildings or towers and is designed to prevent lightning from striking the building or tower). 2. Consider a wire (perfect conductor) of length placed in a uniform electric field that is oriented along the length of the wire. (a) Describe qualitatively what the charge distribution on the wire looks like and sketch

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Unformatted text preview: electric ﬁeld lines and equipotentials for the wire. Now assume that we place two thin wires of the same length, ‘ , end-to-end but not quite touching. This is called a “dipole antenna.” The ends of the wires closest to each other are called the “antenna feed” and they are the terminals where we would place a transmitter or receiver. (b) Assuming that the presence of the two wires do not inﬂuence each other (so that the ﬁeld distributions for each are the same you found for a single wire above), determine the voltage between the terminals of the dipole antenna in terms of the ﬁeld ~ E and the antenna length 2 ‘ . 3. A sphere of radius R carries a polarization, ~ P = k r ˆ r where k is a constant and r is the distance from the center of the sphere. (a) Find the bound charges, σ b and ρ b . (b) Find the ﬁeld inside and outside the sphere. 4. Cheng, P.3-22 . 5. Cheng, P.3-26 . 6. Cheng, P.3-28 ....
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ECE3209-2009-hw4 - electric ﬁeld lines and equipotentials...

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