A laboratory electromagnet consists of a long solenoid of total length with tightly…
PHYSICS · Multi-part · CBSE · Physics · Moving Charges and Magnetism · Moving Charges and Magnetism
Problem
A laboratory electromagnet consists of a long solenoid of total length L with N tightly wound turns carrying a steady current I. The interior of the solenoid is partially filled with a ferromagnetic core of length L1 and relative permeability μr, while the remaining length L2=L−L1 contains only air.
Assume the magnetic field intensity H is uniform within each region and that fringing effects at the ends of each region can be neglected.
(a) Derive expressions for the magnetic flux density B1 in the core‐filled section and B2 in the air‐filled section in terms of μ0,μr,N,I, and L.
(b) Develop an expression for the average magnetic flux density ⟨B⟩ along the entire axis of the solenoid.
(c) For the special case L1=21L and μr=1000, determine the ratio Bair⟨B⟩, where Bair is the field that would exist everywhere inside the solenoid if no core were present.
(d) Discuss two practical design considerations that this analysis suggests when constructing electromagnets that employ only a partial ferromagnetic core.