HW4SP12 - z = -d /2 and the upper plate at z = + d /2. The...

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Physics 4322 Homework Set 4 February 7, 2012 Due: Tuesday, February 14, 2012 1. A long coaxial cable carries current I with current down the surface of the inner cylinder of radius a and back along the outer cylinder of radius b . (See Figure 7.39, page 319 in your text.) Assume that the conductors are held at potential difference V and calculate the energy transported down the cables using the Poynting theorem. 2. Refer to problem 7.31, the one I did as an example in class. Calculate the electric and magnetic fields as functions of the distance s from the axis and the time t . 3. Refer to problem 2 and calculate the energy density u em and the Poynting vector S in the gap. Don't worry about the fringing fields. 4. Consider two equal point charges q , separated by a distance 2 a . Integrate the Maxwell stress tensor over a plane equidistant from the two charges to determine the force of one charge on the other. 5. Consider an infinite parallel-plate capacitor with the lower plate at
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Unformatted text preview: z = -d /2 and the upper plate at z = + d /2. The lower plate carries a charge density -σ and the upper plate carries a charge density + . Determine all nine elements of the stress tensor and use them to determine the force on the upper plate. 6. Show that the standing wave f ( z , t ) = A sin ( kz ) cos( kvt ) satisfies the wave equation and express it as the sum of a wave traveling along + z and one traveling along -z . (Hint: You will need a trigonometric identity.) 7. Consider two wave functions given by the following expressions: f 1 ( z , t )=4 sin[2 π (0.2 z- 3 t )] and f 2 ( z , t )=(1/2.5) sin(7 z + 3.5 t ). For each wave, calculate the angular frequency, propagation number, period, amplitude, speed, and direction of propagation. 8. Write the expression for a harmonic wave of amplitude 10 3 V/m, period 2.2 × 10-15 s, and speed 3 × 10 8 m/s. The wave propagates in the negative x-direction and has a value of 10 3 V/m at t = 0 and x = 0....
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This note was uploaded on 02/20/2012 for the course PHYS 1101 taught by Professor Lowellwood during the Fall '10 term at University of Houston.

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