Consider the uniform magnetic field shown:

Starting from point P and without leaving the region of magnetic field, is it possible to choose a closed path (that is, a path that returns to P) for which the line integral of the magnetic field is nonzero?

Options

A. Yes, but only anti clockwise
B. Yes, but only clockwise
C. Yes, both anti clockwise and clockwise
D. No

Answer

D

Explanation

Any path can be broken into small horizontal and vertical segments. Because the magnetic field is horizontal only be horizontal segments contribute to the line integral. Moving away from P and then returning to it, involves as many horizontal segments to the left as horizontal segments to the right and so the net contribution is always zero.