A rectangular loop and a circular loop are moving out of a uniform magnetic field to a field-free region with a constant velocity. The field is normal to the plane of both loops. Draw the expected shape of the graphs showing the variation of the flux with time in both cases. What is the cause of the difference in the shape of the two graphs?
Solution
While a loop is fully inside the field the flux is constant; as it leaves, the flux falls to zero. Rectangular loop: as it crosses the boundary at constant speed, the area still in the field decreases at a constant rate, so ϕ versus t is a straight line of constant negative slope (constant induced emf). Circular loop: the length of the boundary chord inside the field changes as the circle crosses, so the area leaves the field at a non-uniform rate; ϕ versus t is a curve (the emf is not constant). Cause of the difference: for the rectangle dA/dt is constant, whereas for the circle dA/dt varies during the exit, which changes the shape of the ϕ–t graph.
