A rectangular wire loop of length ℓ and width w is pulled with a constant speed v out of a region of uniform magnetic field B. The field is normal to the plane of the loop and exists over a region whose length along the direction of motion is greater than ℓ but whose width is exactly w. The leading edge of the loop leaves the magnetic field at time t=0. Neglect the resistance of the connecting wires; the loop has total resistance R.
(i) Obtain an expression for the magnetic flux linked with the loop as a function of time for 0≤t≤t1, where t1=ℓ/v.
(ii) Hence derive the induced emf as a function of time in the same interval and indicate its direction.
(iii) Calculate the total charge that flows through the loop while it is leaving the field.
(iv) Show that the total electrical energy dissipated in the loop is equal to the mechanical work done in pulling it out of the field.