fred places two circular loops of conducting wire, one large(radius R) and one small (radius r),
on a horizontal table such that they are centred at the same point.He arranges the larger loop
to carry a constant current I clockwise (when viewed from above).In order to induce a current
in the smaller loop, fred then lifts the smaller loop verticallyupwards at a constant speed v,
without changing its orientation.
1 - Explain why fred is correct to expect an induced current in thesmaller loop, and determine which way this current will flow.
2 - Show that the emf induced in the small loop isapproximately
E = (U_03IR^2v/2z^4)*PIr^2
where z is the height above the table. You may use the result thatthe magnetic field
along the z-axis produced by the large loop is B = µ_0IR^2/2z^3.Make sure to explain,
with the aid of a diagram, the simplifying assumptions you need tomake.
3 - Meanwhile sam, who is also in the room, happens to belevitating upwards at the same
velocity as the small loop. Thus the small loop is stationary inher frame. Explain,
from sam’s point of view, why she should also expect to see aninduced emf in the small
loop. Your explanation should comment on the differences betweenfred’s and sam’s
description of the cause of the emf and explain how it is that theycan both be correct.
