Question

A coil of N turns and area A, carrying a constant currentI, flips in an external magnetic field Bext from having its dipole moment µµµ opposite Bext to alignment with that field. As a result, the magnetic flux through the coil corresponding tothe external field Bext changes from Φext = −Bext A to Φext =+ Bext A. Calculate the total work which the coil’s power supply must do against the resulting induced EMF to maintain constant current I through the coil during this process. HINT: Consider the flip process to consist of a sequence of small time intervals ∆t, and add up the work done during each of these intervals

Answer 1

Power supplied against induced emf = Ei

E is induced emf and i is constant current in loop.

Induced emf in the loop over small time interval

delta t , E = (delta phi)/(delta t)

Hence power supplied against induced emf over this time interval = i*(delta phi) / (delta t)

Work done against induced emf over this time interval = i*(delta phi)

Total work done = sum of small works

= i* sigma (delta phi)

= i * (total change in flux )

= i * ( 2 B_{​​​​​​ext} A) = 2 B_{​​​​​​ext} Ai