A circular loop of radius `r` moves with a constant velocity `v` in a region with uniform magnetic field `B`. Calculate the potential difference between two points `(A, B)`, `(C, D)`, and `(E, F)` located on the loop.

Explanation

This illustration highlights a very common misconception in students. We know that when a closed loop translates in a uniform magnetic field, the net emf induced in the loop is zero. Students jump to the conclusion that the potential difference acroos any two points on the loop should also be zero. This are on a diameter that is oriented perpendicular to the direction of motion of the loop. Since net induced emf is zero there will be no induced currents in the loop. we can, therefore, cut the loop along the diameter `AB` and divided it into two semicircular loop without affectiving the physics of the problem. Each of these loop can in turn be replaced by straight conductors of length `2r`. The induced emf across each of these conductors is `B(2r)v` and the potential difference across `AB` is `B(2r)v`. Note that when we travel through the whole circuit, the net induced emf is still zero as the two emf s cancel each other. In a similar manner, we can show that the potential difference between `E` and `F` is `2Brv sin theta` where `theta` is the angle between line `EF` and the difference between `C` and `D` will be zero because `theta = 0^(@)` for this case.