Which of the following assumptions is/are valid for electromagnetic induction to happen in the Earth?
Show Hint
- Plane-wave approximation of the inducing field
- Displacement currents are not neglected
- Earth behaves as Ohmic conductor due to conservation of charge
- Earth does not generate electromagnetic energy, but only absorbs or dissipates it
The Correct Option is A, C, D
Solution and Explanation
In magnetotelluric (MT) and geomagnetic depth-sounding theory, EM induction in the Earth rests on a set of standard simplifying assumptions. Check each option against them.
Step 1 - Plane-wave approximation: The natural source currents (ionospheric and magnetospheric current systems) sit far above the Earth's surface compared with the induction scale lengths involved, so at the surface the primary field can be treated as a uniform, vertically incident plane wave. This is a foundational assumption of MT theory, so (A) is correct.
Step 2 - Displacement currents: MT induction operates in the quasi-static (diffusive) regime because Earth materials are relatively good conductors and the frequencies used are low. Here the conduction current density \(\sigma E\) dominates the displacement current density \(\epsilon \partial E/\partial t\) by many orders of magnitude, so displacement currents ARE neglected, not retained. The statement "displacement currents are not neglected" is therefore FALSE, so (B) is incorrect.
Step 3 - Ohmic behaviour: Applying Ohm's law \(\mathbf{J}=\sigma\mathbf{E}\) together with charge conservation (the continuity equation \(\nabla\cdot\mathbf{J}=-\partial\rho/\partial t\)) shows that any free charge in a conductor relaxes away almost instantaneously, so the Earth behaves as a pure Ohmic conductor. This matches (C), which is correct.
Step 4 - Passive medium: The Earth has no internal EM source in this problem; it only responds to the externally imposed inducing field, dissipating the energy resistively (Joule heating) rather than generating any of its own. This matches (D), which is correct.
The valid assumptions are (A), (C) and (D). \(\boxed{A,\ C,\ D}\)
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