Question

The ???? − i relationship for an electromagnetic system is given by ???? = 1.2i1/2 g where g is the air-gap length. For current i = 2 A and g = 10 cm, determine the mechanical force on the moving part

(a) Using the energy of the system
(b) Using the coenergy of the system

Answer 1

a) The mechanical force is -226.2 N

b) Using the coenergy the mechanical force is -226.2 N

Step-by-step explanation:

a) Energy of the system:

`\lambda =(1.2*i^(1/2) )/(g) \\i=((\lambda g)/(1.2) )^(2)`

`(\delta w_(f) )/(\delta g) =(g^(2)\lambda ^(3) )/(3*1.2^(2) )`

`f_(m)=- (\delta w_(f) )/(\delta g) =-(g^(2)\lambda ^(3) )/(3*1.2^(2) )`

If i = 2A and g = 10 cm

`\lambda =(1.2*i^(1/2) )/(g) =(1.2*2^(1/2) )/(10x10^(-2) ) =16.97`

`f_(m)=-(g^(2)\lambda ^(3) )/(3*1.2^(2) )=-(16.97^(3)*2*0.1 )/(3*1.2^(2) ) =-226.2N`

b) Using the coenergy of the system:

`f_(m)=- (\delta w_(f) )/(\delta g) =-(1.2*2*i^(3/2) )/(3*g^(2) )=-(1.2*2*2^(3/2) )/(3*0.1^(2) ) =-226.2N`