Kevin Zhou — Advanced E&M IV Problem 3 · Kevin Zhou #E8.3
Physics · electromagnetism
Problem
Problem 3. A version of the method of images, introduced in E2, works for dielectrics. Let’s
suppose there is vacuum at z > 0, a dielectric κ at z < 0, and a point charge q a distance d above
3
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the plane z = 0. We need to find the surface bound charge density σ that appears on the plane.
b
(a) Let Ez be the z-component of the electric field due to the point charge alone. At a given
0
point just below the plane z = 0, find Ez in terms of Ez and σ .
0 b
(b) Use this result to solve for σ in terms of Ez and κ.
b 0
(c) Your answer will be exactly the same as what one gets for a conductor at z < 0, multiplied
by a κ-dependent constant. Using this information, characterize the image charge and find
the force on the real charge.