Induction by a horizontal oscillating magnetic dipole over a conducting homogeneous Earth

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Abstract
The magnetic field of an oscillating horizontal magnetic dipole on the surface of a homogeneous Earth is calculated. For lower frequencies, where displacement currents can be neglected, the magnetic field on the surface of the Earth can be represented in terms of transcendental and cylindrical functions. Particular attention is paid to the vertical component, which vanishes as the conductivity of the Earth approaches zero. An explicit formula is given for the value of this component in parametric form involving the conductivity, frequency, and distance to the observer. The magnetic field components tangential to the Earth's surface are also considered.

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