A long, tightly wound primary solenoid with turns is wrapped uniformly around a…
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
A long, tightly wound primary solenoid with 500 turns is wrapped uniformly around a cylindrical ferromagnetic core of radius 1.0cm. Starting at t=0, the current in the primary is adjusted so that the magnetic field inside the core follows the time dependence
B(t)=1.5×10−2t2T(0≤t≤3.0s).
A secondary coil of 120 turns is wound coaxially over the same core and connected to a 10Ω resistor. Assume the magnetic field is uniform and confined entirely within the core.
(a) Derive an expression for the magnetic flux through the secondary coil as a function of time over the given interval.
(b) Obtain the instantaneous emf induced in the secondary coil as a function of time.
(c) Write an expression for the instantaneous power dissipated in the 10Ω resistor.
(d) Calculate the total energy dissipated in the resistor from t=0 to t=3.0s.