ECE135_2010SPRING_EXAM1_PROFSOLN_[0]

# ECE135_2010SPRING_EXAM1_PROFSOLN_[0] - charge densities +...

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ECE 135 Winter 2010 1. [10 points] Two spherical cavities of radii “a” and “b” are hollowed out from the interior of a (neutral) conducting sphere of radius R. At the center of each cavity there are two point charges of magnitudes a q and b q respectively. Refer to Fig. 1 for details. a) Find the surface charges b a σ , and . R b) What is the field outside the conductor? c) What is the field within each cavity? d) What is the force on a q and b q ? e) Which of these answers would change if a third charge c q were brought near the conductor? 2. [10 points] Find the mutual capacitance per unit length between two thin, parallel (electrically conducting) wires, each with a circular cross-section but its own diameter. Refer to Fig. 2 for details. 3. [10 points] Two infinitely long wires running parallel to the x-axis carry uniform

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Unformatted text preview: charge densities + and .-Refer to Fig. 3 for details. a. Find the potential at any point (x, y, z) using the origin as your reference. b. Show that the equipotential surfaces are circular cylinders and locate the axis and the radius of the cylinder corresponding to a given potential . V 4. [10 points] A large parallel-plate capacitor with uniform surface charge on the upper plate and -on the lower plate is moving with a constant speed , v as shown in Fig. 4. a. Find the magnetic field between the plates and also above and below them. b. Find the magnetic force per unit area on the upper plate, including its direction. c. At what speed, would the magnetic force balance the electrical force. Figure 1 Figure 2 Figure 3 Figure 4...
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## This note was uploaded on 02/27/2012 for the course CHEMISTRY/ CH/ECE/PH/ taught by Professor Faculty during the Spring '08 term at Cooper Union.

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ECE135_2010SPRING_EXAM1_PROFSOLN_[0] - charge densities +...

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