# HW84_6 - is forced to be zero An infinitesimal dipole is...

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Electromagnetics School of Electrical and Computer Engineering University of Tehran Homework 6 Fall Semester 1384 Due 84/9/21 Problem 1 a) Explain why the magnetic susceptibility of a diamagnetic material is negative. b) Explain why the magnetic susceptibility of diamagnetic materials is independent of temperature. c) A sample of an unknown magnetic material is available. Devise a technique to determine whether this material is diamagnetic or paramagnetic. Problem 2 Assume that the plane 0 = z is a conducting plate of infinite extent. It is kept at zero voltage. The region 0 > z is free space. A point charge q is located at ) , 0 , 0 ( h with 0 > h . Denote the surface charge induced on the conducting plate by ) , ( y x s ρ . a) Determine ) , ( y x s . b) Using the obtained ) , ( y x s , show mathematically that ∫∫ = q dxdy y x s ) , ( . c) Repeat (a) and (b) when the region 0 > z is filled with a dielectric of susceptibility χ . Problem 3 Plane 0 = z is a conducting plate of infinite dimensions. The plate is grounded, i.e., its potential

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Unformatted text preview: is forced to be zero. An infinitesimal dipole is located above the plane at ) , , ( h with > h . At the observation point r r , obtain the electric potential produced by the dipole a) when its dipole moment is z p p o ˆ = r , and b) when its dipole moment is x p p o ˆ = r . c) Simplify the above results when r h r << . Problem 4 Assume two grounded infinite copper plates located at h z − = and h z = with > h . A point charge q is located at ) , , ( . Find the location and value of image charges for this configuration. What is the total charge induced on each plate? Problem 5 Suppose that the half space ≤ z is occupied by a dielectric material the susceptibility of which is χ . The upper half space > z is free space. A surface charge having a constant density of s ρ is positioned at the plane h z = in the upper half space. Determine the polarization vector in the lower half space. M. Shahabadi...
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HW84_6 - is forced to be zero An infinitesimal dipole is...

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