Assignment2 - conducting sphere that is close to a grounded...

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EE 501 Wave Propagation and Radiation Assignment Two: covers electric potential, method of images, boundary value problems 1. Determine the E field both inside and outside a spherical cloud of electrons with a uniform volume charge density ρ =- ρ 0 ( where ρ 0 is a positive quantity) for 0≤R ≤b and ρ= 0 for R>b by solving both Poisson’s and Laplace’s equations for V. 2. Assume that the z = 0 plane separates two lossless dielectric regions with r1 = 2 and r2 = 3. If we know that E 1 in region 1 is a x 2y a y 3x + a z (5+z), what do we also know about E 2 and D 2 in region 2? Can we determine E 2 and D 2 at any point in region 2? 3. Using the method of images, derive the expression for the potential of a charged
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Unformatted text preview: conducting sphere that is close to a grounded conducting plane. 4.An infinitely long thin conducting circular tube of radius b is split in two halves. The upper half is kept at potential V=V . The lower half at V=-V 0. Determine the potential distribution both inside and outside the tube. 5.Find the capacitance per unit length between a cylindrical conductor of radius a=2.5cm and a ground plane parallel to the conductor axis and a distance h=6m from it. 6. A point charge exists at a distance d above a large grounded conducting plane. Determine a) the surface charge density s and b) the total charge induced on the conducting planes....
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