Answer to Question 8

 

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The diagram shows a piece of magnetic material of relative permeability 130.

 

The dimensions are shown on the diagram.  Calculate:

(a) The Magnetomotive force;

(b) The reluctance for Loop 1;

(c) The reluctance for Loop 2;

(d) The total reluctance;

(e) The total flux;

(f) The flux in Loops 1 and 2.

(g) Are the fluxes consistent?  Explain your answer.

 

 

(a) Fm = 250 turns 2.5 A = 625 A turns

 

(b) Formula:

A = 1.5 10-2 m 2.0 10-2 m = 3.0 10-4 m2

m = 4p 10-7 H m-1 130 = 1.634 10-4 H m-1

 

S1  = 0.35 m (1.634 10-4 H m-1 3.0 10-4 m2) = 7.140 106 H-1 = 7.1 106 H-1 (2 s.f.)

 

(c) Formula:

A = 1.0 10-2 m 2.0 10-2 m = 2.0 10-4 m2

 

S2  = 0.30 m (1.634 10-4 H m-1 2.0 10-4 m2) = 9.180 106 H-1 = 9.2 106 H-1 (2 s.f.)

 

 

(d) Formula:

(Stot)-1 = (7.140 106 H-1 )-1  + (9.180 106 H-1 )-1 = 2.490 10-7 H

 

Stot = 4.016 106 H-1 = 4.0 106 H-1 (2 s.f.)

 

(e) Formula:

 

 Ftot  = 625 A turns  4.016 106 H-1  = 1.56 10-4 Wb = 1.6 10-4 Wb (2 s.f.)

 

(f) F1  = 625 A turns  7.140 106 H-1 = 8.75 10-5 Wb = 8.8 10-5 Wb (2 s.f.)

      F2  = 625 A turns  9.180 106 H-1 = 6.81 10-5 Wb = 6.8 10-5 Wb (2 s.f.)

 

(g) Ftot  = 8.75 10-5 Wb + 6.81 10-5 Wb = 1.556 10-4 Wb

     The calculation shows that the answers are consistent.