Answer to Question 1

 

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A toroidal (dough-nut shaped) piece of magnetic material has a relative permeability of 200.  It is 7.5 cm in radius and has a a circular cross section of radius 1.0 cm.  Calculate the reluctance.

A = p (1.0 10-2 m)2 = 3.14 10-4 m2

 

l = 2 p 7.5 10-2 m = 0.471 m

 

S = (2 p 7.5 10-2 m) [4 p 10-7 H m-1 200 3.14 10-4 m2] = (2 7.5 10-2 m) [4 10-7 H m-1 200 3.14 10-4 m2] = 6.0 106  H-1