Engineering Electromagnetics with CD (McGraw-Hill Series in Electrical Engineering)

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EE 151 Caltech Electromagnetic Engineering Spring ‘05 Homework 1 Due Tuesday, April 5 th in class 1. A uniform line charge 2 μC/m is located on the z axis. Find E in Cartesian coordinates at P (1,2,3) if the charge extends from : ( a ) z = - to z = ; ( b ) z = -4 to z = 4. 2. Within the spherical shell, 3 < r < 4 m, the electric flux density is given as D = 5( r - 3) 3 a r C/m 2 . ( a ) What is the volume charge density at r = 4? ( b ) What is the electric flux density at r = 4? ( c ) How much electric flux leaves the sphere r = 4? ( d ) How much charge is contained within the sphere r = 4? 3. A parallel plate capacitor consists of two perfect conducts separated by a distance x. The dielectric constant of the medium in between the two plates is
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Unformatted text preview: ε . The area of the two plates A is large enough so that the fringe effect is negligible. The mass of each plate is m. The upper plate is allowed to move up and down, but not horizontally. The lower plate is fixed on the substrate. A +Q x +Q Figure 1 Calculate the charge Q necessary to keep the upper plate at rest. 4. Using the fact that E → = kq (r → 1 – r → 2 ) / |r → 1 – r → 2 | 3 , V = kq (1/ |r → 1 – r → 2 |), prove that → ∇ × E → = 0 and E → ±±± = -∇ V. 5. Use Femlab to plot the magnitude of the E-field for the following two systems. The plates are assumed to be perfect conductors. ( a ) ( b )...
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  • Spring '05
  • Psaltis
  • Electromagnet, Electric charge, Fundamental physics concepts, 4 m, Electric Flux Density, Electromagnetic Engineering

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