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An infinitely long straight wire lying along the x-axis (in the xy-plane) carries a current i = i0*t/T directed along +x, where i0 and T are positive constants and t is time. Consider a field point on the +y-axis at the origin's neighbourhood (just off the wire, on the +y side). Which statement is correct?

1. The displacement current near the point is in the +y direction.
2. The induced electric field at the point is in the -x direction.
3. The Poynting vector (E x B)/mu0 points toward the wire (in the -y direction).
4. The magnetic field at the point is in the +z direction.

Correct answer: The Poynting vector (E x B)/mu0 points toward the wire (in the -y direction).

Solution

B from a wire along +x, at a point on the +y side, is along -z (right-hand rule). The increasing current produces an induced electric field that opposes the increase, i.e. antiparallel to the current, so E is along -x. Then S = (E x B)/mu0 = ((-x) x (-z))/mu0-direction = (x x z)/mu0-direction = -y (since x x z = -y). So the Poynting vector points in -y, toward the wire, consistent with magnetic energy flowing into the growing field region.

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