Question 4 of 8: Time-Domain EM — Large-Loop Transmitter and Plate Response

Question 4: Time-Domain EM — Large-Loop Transmitter and Plate Response (7 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Approach. Apply Lenz's law (induced eddy currents always oppose the change in flux that created them) and the coupling rule that a conductor couples most strongly to a field when the field threads perpendicular through its LARGEST face (broadside) and most weakly when the field runs along its plane (edge-on).

(a) Current direction. The exam figure shows $\overline{H}_p$ pointing DOWNWARD (into the ground) directly under the loop. By the right-hand rule, a downward field inside the loop requires the current to flow clockwise when the loop is viewed from above (i.e. from outside/above looking down along $\overline{H}_p$'s direction) — marked with the arrow $I$ on the near edge of the loop in the figure below.

(b) Weakly- vs. strongly-coupled plates. Plate #1 is drawn standing vertically, edge-on to $\overline{H}_p$ (its large face parallel to the vertical field lines) — almost no flux threads through it, so it is very weakly coupled. Plate #2 is drawn horizontal, directly beneath the loop, broadside to $\overline{H}_p$ — the field lines thread straight through its largest face, so it is very strongly coupled. (A plate's coupling depends only on its ORIENTATION relative to $\overline{H}_p$, not on its lateral position under the loop, since $\overline{H}_p$ is broadly vertical throughout the region shown.)

(c) Eddy currents and secondary field at shut-off. By Lenz's law, the eddy currents induced in Plate #2 the instant the primary current is switched off flow in the SAME sense as the (now-vanishing) transmitter current, so as to try to maintain the collapsing downward flux through the plate — i.e. also clockwise viewed from above, concentrated as a current loop around the plate's perimeter (sketched as the closed loop $i_e$ in the figure). These eddy currents in turn produce their own secondary field $\overline{H}_s$, which by the same right-hand rule points DOWNWARD inside the eddy-current loop (reinforcing $H_p$ there, opposing its collapse) and loops back UPWARD outside the loop — the classic magnetic-dipole pattern of a current loop, shown as the arced field lines above Plate #2.

(d) $H_{sz}$ profile along A–B. Because the eddy-current loop's secondary field is a vertical dipole centred on Plate #2, the VERTICAL component $H_{sz}$ measured along a surface profile shows the classic single-plate TDEM signature: strongly NEGATIVE directly over the plate (secondary field pointing down, same sense as $H_p$, dominates), decaying and crossing through zero near the plate's edge, then a smaller POSITIVE lobe just beyond the edge (where the return, upward-looping flux from the eddy-current dipole dominates), decaying back toward zero further from the loop.