Question #93303

1 Answer
Apr 24, 2014

For part of the loop, dl is in the same direction as the magnetic field and for a different part of the loop, dl is opposite the magnetic field (so the dot product of B and dl is negative). You are correct that the enclosed current is zero, but that just means that when you add the pieces up around the loop, they add to zero.

For simplicity let the loop be a square with sides of length L and with the left and right sides parallel to B. When you look at the top and bottom pieces, adding up $\int B \cdot \mathrm{dl}$ is zero because B and dl are perpendicular to each other. For one of the sides $\int B \cdot \mathrm{dl} = + B L$ since B and dl are in the same direction and for the other side $\int B \cdot \mathrm{dl} = - B L$ since B and dl are in opposite directions so when you add all the pieces together around the loop you get zero. It does not mean that B is zero.