The forward solution given by Hesse et al. is incorrect. The error is a result of the erroneous governing differential equation [their equation (2)], which for the only nonzero component of the magnetic field has the following form:
Unfortunately, the authors did not show how they arrived at this equation, but the mistake is so frequently encountered that its origin can be reconstructed quite easily. Indeed, by neglecting displacement currents in the fourth Maxwell equation and by applying the vector operator × to both parts of the equation, we obtain
Making use of the well known vector identity
and of the first and third Maxwell equations, we obtain
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