Line Sources at a Material Interface

Use image sources to solve the field of a uniform line charge above a dielectric half-space, then switch to the dual magnetic line-current problem.

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alpha_E = (epsilon1 - epsilon2) / (epsilon1 + epsilon2)
lambda_img = alpha_E lambda, lambda_t = 2 epsilon2 lambda / (epsilon1 + epsilon2)
alpha_M = (mu2 - mu1) / (mu1 + mu2)
I_img = alpha_M I, I_t = 2 mu1 I / (mu1 + mu2)

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Problem

Electric Magnetic

epsilon1 / epsilon2 3.00 Source height 0.90 a Field lines 32 Equipotential contours 15

Potential color Equipotential contours Field lines Image construction

Electric line charge

epsilon1 / epsilon2 = 3.02

lambda_img / lambda = 0.503

lambda_t / lambda = 0.497

Phi is continuous; epsilon E_z is continuous at z = 0.

Potential and field map