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Two situations each show an electric field vector E together with an induced magnetic field line around it (see figure). For each case, decide whether the magnitude of E is increasing or decreasing, based on the direction of the induced B.

1. increasing in (a) and decreasing in (b).
2. increasing in (a) and (b).
3. decreasing in (a) and (b).
4. decreasing in (a) and increasing in (b).

Correct answer: increasing in (a) and decreasing in (b).

Solution

By the Ampere-Maxwell law, the induced magnetic field circulates around dE/dt according to the right-hand rule (curl your fingers in the B direction; the thumb points along dE/dt). Reading the given B circulation directions: in case (a) the induced B is consistent with dE/dt pointing the same way as E, so |E| is increasing; in case (b) the B circulation corresponds to dE/dt opposite to E, so |E| is decreasing. Hence E is increasing in (a) and decreasing in (b).

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