Question

Fig. illustrates plane figures made of thin conductors which are located in a uniform magnetic field directed away from a reader beyond the plane of the drawing. The magnetic induction starts diminishing. Find how the currents induced in these loops are directed.

Answer 1

(a) Outer loop: counterclockwise (chord’s net current is from right to left).
(b) Counterclockwise.
(c) Outer loop: counterclockwise (the inner loop’s counterclockwise emf is “partially cancelled” on the common segment, so the net current follows the outer loop’s counterclockwise sense).
(d) In each lobe the induced current is counterclockwise.

Answer 2

Because the external magnetic field (directed “out of the page”) is decreasing, Lenz’s law tells us that the induced currents must act so as to oppose this decrease. This means that they must “try” to produce a field also pointing out of the page. By the right‐hand rule a current that produces an out–of–page field circulates counterclockwise.

In the figures the conductors form more than one loop, so one must “assign” a counterclockwise current to every independent closed path. In (a) and (c) two loops share a common segment. Then, although each loop “wants” a counterclockwise current, the net current in the common branch is the difference of the two loop currents (the larger loop, having a larger induced emf, dominates). In (b) and (d) there is no common branch problem.

(a) The “big” (outer) loop has an induced counterclockwise current; thus along the common chord the net current is directed from right to left.
(b) The complete loop has an induced current circulating counterclockwise.
(c) The outer loop (which encloses a larger area) is driven counterclockwise; the inner “loop” (formed by the two arcs of the inner circle) would individually be counterclockwise, but since its current opposes that in the common segment, the net current in the common part is that of the outer loop (counterclockwise).
(d) In the figure‐8, each lobe has its own induced current circulating counterclockwise.