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117-11HMWRK2 - Find the surface charge density ρ s 2...

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Prof. E. Yablonovitch ELECTROMAGNETIC FIELDS AND WAVES EE117 Homework #2; assigned: Feb. 7, 2011 Due 5PM, Monday, Feb. 14, 2011 Please put the completed homework in the plastic tray on my door, 267M Cory 1. An infinitely long conducting cylinder of radius a , has a surface charge density of ρ s . The cylinder is surrounded by a dielectric medium with ε r =4 and contains no free charges. To induce charges on the metal surface, an external electric field must be applied. The tangential component of the electric field in the region r>a caused by the surface charges is 2 / cos ˆ r E t φ φ = where φ ˆ is a unit vector in the tangential direction. Since a static conductor cannot have any tangential field, this must be cancelled by the externally applied electric field.
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Unformatted text preview: Find the surface charge density, ρ s . 2. Problem 4.58 on page 233 of Ulaby 6 th edition. 3. You have a 20cm × 30cm rectangular loop of wire carrying 10Amps dc. What is the magnetic field in the center of the loop? 4. Problem 5.4 on page 274 of Ulaby 6 th edition. 5. Do Problem 5.17 on page 277 of Ulaby 6 th edition. 6. You are making electrical contact using the very large hemispherical electrode below. Contact is made to a tiny hemispherical protrusion of diameter 100nm shown in red below. What is the contact resistance of this electrode? Please take the Ag, Silver, resistivity as 2 × 10-8 Ohm-meters. ∞ 100nm Ag...
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