A square conducting loop of side and resistance is initially completely outside a…
PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A square conducting loop of side a and resistance R is initially completely outside a large region of uniform magnetic field of magnitude B. The plane of the loop is perpendicular to the field and the side of the loop closest to the field is parallel to the boundary of the field region. The loop is now pulled with constant speed v so that it enters the field completely.
(i) Derive an expression for the magnetic flux linked with the loop as a function of the distance x that the leading edge has penetrated into the field region (0≤x≤a).
(ii) From the result of (i), obtain the expression for the induced emf E(x) and the induced current I(x) during the entry phase. Clearly state the sense of the current.
(iii) Show that the total mechanical work done in pulling the loop fully into the field equals the total heat produced in the loop during the same interval, thereby verifying energy conservation.