Imagine that, at a certain point in empty space, the curl of the magnetic field has a positive $x$ component. What can we conclude from this information?
A) $E_{x}$ must be positive at that point.
B) $E_{x}$ must be negative at that point.
C) $E_{x}$ must be zero at that point.
D) $E_{x}$ must be increasing with time at that point.
E) $E_{x}$ must be decreasing with time at that point.
F) The magnetic field described is not physically possible.
G) None of the above.

Question

Quizplus · Accepted Answer

EMaxwell's equations, specifically Faraday's Law of Induction, state that a changing magnetic field induces an electric field. The curl of the magnetic field being nonzero implies a changing magnetic field, which in turn induces an electric field. The direction (positive or negative) of $E_x$ is not specified by the information given, but its time derivative must be nonzero, indicating it is changing over time. This could mean $E_x$ is either increasing or decreasing, hence both D and E are correct.

Imagine That, at a Certain Point in Empty Space, the Curl