HW84_5 - a r ≤< Problem 3 Electric dipoles occupy the...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Homework 5 Fall Semester 1384 Due 84/8/23 Problem 1 Use the uniqueness theorem to prove that the electric field inside an infinitely thin, uniformly charged spherical shell is zero. Assume that inside and outside the spherical shell is vacuum. (Hint: Firstly, use the symmetry of the configuration to show that the tangential component of the electric field must vanish on the inner boundary of the shell.) Problem 2 In free space, in the region a r 0 of a spherical coordinate system, magnetic dipoles are distributed in such a way that their magnetization vector can be expressed as: r M r a M o ˆ 2 = r [ A/m ] in which o M is a constant with a unit of A/m . a) Find the magnetic field and the magnetic field intensity everywhere in space. b) Is there any discontinuity at a r = in the obtained fields? Explain. c) Repeat (a) and (b) when the above magnetization vector is limited to the region
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Unformatted text preview: a r ≤ < . Problem 3 Electric dipoles occupy the region R r < of the spherical coordinate system such that their polarization vector can be described by z P P o ˆ = r with o P as a constant. Assume free space everywhere, and obtain the value of the closed surface integral ∫ ∂ ⋅ V S d E r r in which E r is the electric field produced by the dipoles, and V is the volume of a hemisphere of radius R 2 whose center is at the origin and whose north pole is on the z-axis. Problem 4 The resistivity of a conductor is defined as σ = ρ / 1 where σ denotes its conductivity. Show that according to Drude’s model, the resistivity of a conductor increases with the square root of the temperature. (Hint: Consider the mean free path of electrons, that is the distance traveled between two successive collisions.) M. Shahabadi...
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