Where is my mistake? I have a feeling it's in the calculation of B... ?
Do you mean that B is constant inside the rectangle?
It's a given that the rectangle is fixed to the ground..
So apart from the fact that the magnetic field in it changes direction all the time, B's size is constant
So you say that the magnetic field of a current carrying wire does not depend on the distance from the wire?
For a long straight wire, B is proportional to 1/r.
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