Two samples of ferromagnetic material are examined
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Two samples of ferromagnetic material are examined. Each sample is placed in a uniform magnetic field H that is slowly increased from 0 to 0.30kAm−1 and then decreased back to 0. The magnetization M (in kAm−1) of each sample is recorded at several points during the cycle and summarized in the table below.
Sample A (soft iron):
H (kA m−1): 0.00, 0.10, 0.20, 0.30, 0.20*, 0.10*, 0.00*
M (kA m−1): 0, 60, 90, 100, 80, 40, 20
Sample B (hard steel):
H (kA m−1): 0.00, 0.10, 0.20, 0.30, 0.20*, 0.10*, 0.00*
M (kA m−1): 0, 20, 60, 80, 60, 40, –10
(An asterisk * denotes values taken while the field was being reduced.)
Answer the following.
(1) Using the data, determine the remanent magnetization Mr for each sample at H=0 after the field has been reduced.
(2) For each sample, estimate the coercive field Hc—the value of H at which M first becomes zero while the field is being reduced. State any assumptions clearly.
(3) Based on your results, identify which sample is more suitable for the core of a transformer operated at 60 Hz and explain your choice.
(4) Approximate the energy dissipated per magnetization cycle for each sample by treating the hysteresis loop as a rectangle with height 2Mr and width 2Hc. Compute the numerical value of this area (in kA2 m−2) for both samples and interpret your findings.