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# SE_04 - (c Evaluate the surface density of the induced...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Supplementary Exercises 4 Fall Semester 1384 Problem 1 The region 0 > z is free space while the region 0 < z is filled with a homogeneous dielectric. (See the figure below.) A point charge q is located inside the dielectric half-space at the point ) , 0 , 0 ( h . (a) Determine the polarization vector P r at the point ) 2 , 0 , 0 ( h . (b) Determine volume and surface density of the bound charges for the dielectric half-space. (c) Evaluate the total bound charges on the interface 0 = z . Problem 2 See the figure below. Here, a conducting hemisphere is placed on an infinite conducting plate. A point charge q is located at the point ) , 0 , ( b a such that R b a > + 2 2 . (a) Determine the location and value of the image charges. (b) Determine the total induced charges on the conductors.

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Unformatted text preview: (c) Evaluate the surface density of the induced charges at the point ) , , ( R . (d) For far points, how does the potential vary as a function of r (distance to the origin)? (e) For R b a 5 . 1 2 2 = + , draw the field lines qualitatively. z q r ε o ε q z x V o ε Conductor R ) , , ( b a Problem 3 In a coaxial cable the center conductor is misplaced from the center of the cable by a known amount e . According to the shown drawing, the radius of the center conductor is b while the internal radius of the cable shield is a . Determine the capacitance per unit length of the cable when the cable is filled with a dielectric having a relative permittivity of r ε . M. Shahabadi a b e r ε...
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SE_04 - (c Evaluate the surface density of the induced...

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