c.) Assuming that the relative permeability ( mu _(r) ) of the magnetic material remains constant, derive a
new equation (variables only, no values) for the force developed, and show that it is no longer
independent of x. Hint: the mean length of the flux path through the magnetic material is
approximately L~~16a
(4 marks)
d.) Considering the case when x~~0, draw a simple figure in your answer books and illustrate the
flux lines through the core and moveable plunger, paying particular attention to the regions between
the core and moveable plunger (i.e. in and around the bushings). Comment briefly on any
observations which may or may not affect the assumptions generally made with these types of
problems. Hint: also consider the case if the magnetic material was Silicon Steel; refer to the B-H
curve.
(4 marks)
e.) Referring to question 2c above, in a practical implementation of this transducer operating within
a flux-density range from 0T to 1.2T, which material would best be approximated by the assumed
permeability: Silicon Steel or Soft-Cast Steel? Justify your answer. Hint: Refer to the B-H curves.
(2 marks)
Question 2 Consider the transducer below that comprises a magnetic core and moveable plunger,_and two frictionless non-magnetic bushings:
N turns
W +2a+x
Non-magnetic bushing
Movable plunge
a.) Ignoring the magnetic components, derive a simple expression (variables only,no values for the force developed, and show that it remains constant, for all positions of x. (3 marks)
b. Using the above, for the same current, show that the force produced is more sensitive to the
increase in the number of.turns N versus.a 10 % decrease in the thickness Igap of the bushings. (2 marks)
Page 2 of 4
c. Assuming that the relative permeability (, of the magnetic material remains constant, derive a new equation (variables only, no values) for the force developed, and show that it is no longer independent of x. Hint: the mean length of the flux path through the magnetic material is approximately L16a (4 marks)
d. Considering the case when x 0, draw a simple figure in your answer books and illustrate the flux lines through the core and moveable plunger, paying particular attention to the regions between the core and moveable plunger (i.e. in and around the bushings. Comment briefly on any
problems. Hint: also consider the case if the magnetic material was Silicon Steel; refer to the B-H curve. (4 marks)
e.) Referring to question 2c above, in a practical implementation of this transducer operating within a flux-density range from 0 T to 1.2 T, which material would best be approximated by the assumed permeability: Silicon Steel or Soft-Cast Steel? Justify your answer. Hint: Refer to the B-H curves. (2 marks)
[15marksl
