An infinite slab with dielectric constant = / 0 lies between z = a and z

An infinite slab with dielectric constant κ = ε/ε₀ lies between z = a and z = b = a + c. A point charge q sits at the origin of coordinates. Let β = (κ − 1)/(κ + 1) and use solutions of Laplace’s equation in cylindrical coordinates to show that.

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4(z > c) = q(1 - B²) Απερ ∞ S 0 dk Jo(kp) exp(-kz) 1 -B² exp(-2kc) = q(1 - B²) Απερ n=0 B²n (z+2nc)² + p²