We sum the integrand around the loop in the xy-plane, no contribution from the top and bottom, so

• We sum the integrand around the loop in the xy-plane, no contribution from the top and bottom, so

• The magnetic flux through the box is

and the first Maxwell (Faraday) law

then gives

which shows that we can have time-varying fields in the vacuum.

• In the xz-plane, same procedure gives

• We can eliminate either

by differentiating with respect to x or t and we will do the former:

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