Navigation:  Sample Problems > applications > magnetism >

vector_magnet_coil

Print this Topic Previous pageReturn to chapter overviewNext page

{ VECTOR_MAGNET_COIL.PDE  

 

 AXI-SYMMETRIC MAGNETIC FIELDS

 This example is a modification of MAGNET_COIL.PDE using vector variables.

 See that example for discussion of the problem formulation.

}

 

Title 'AXI-SYMMETRIC MAGNETIC FIELD - Vector Variables'

 

Coordinates

  { Cylindrical coordinates, with cylinder axis along Cartesian X direction }

   xcylinder(Z,R)  

 

Variables

   A = vector(0,0,Aphi) { the azimuthal component of the  vector potential }

 

Definitions

   mu = 1                     { the permeability }

   rmu = 1/mu

   current = 0                 { the source defaults to zero }

   J = vector(0,0,current)

   Bz = dr(r*Aphi)/r

 

Initial Values

   Aphi = 2                   { unimportant unless mu varies with H }

 

Equations

  { FlexPDE expands CURL in proper coordinates }

   A : curl(rmu*curl(A)) = J  

 

Boundaries

  Region 1

    start(-10,0)

    value(Aphi) = 0           { specify A=0 along axis }

      line to (10,0)

    natural(Aphi) = 0         { H<dot>n = 0 on distant sphere }

      arc(center=0,0) angle 180 to close

 

  Region 2

     current = 10             { override source value in the coil }

    start (-0.25,1)

      line to (0.25,1) to (0.25,1.5) to (-0.25,1.5) to close

 

Monitors

  contour(Bz) zoom(-2,0,4,4) as 'FLUX DENSITY B'

  contour(Aphi) as 'Potential'

 

Plots

  grid(z,r)

  contour(Bz) as 'FLUX DENSITY B'

  contour(Bz) zoom(-2,0,4,4) as 'FLUX DENSITY B'

  elevation(Aphi,dr(Aphi),Aphi/r,dr(Aphi)+Aphi/r,Aphi+r*dr(Aphi))  

      from (0,0) to (0,1) as 'Bz'

  vector(dr(Aphi)+Aphi/r,-dz(Aphi)) as 'FLUX DENSITY B'

  vector(dr(Aphi)+Aphi/r,-dz(Aphi)) zoom(-2,0,4,4) as 'FLUX DENSITY B'

  contour(Aphi) as 'MAGNETIC POTENTIAL'

  contour(Aphi) zoom(-2,0,4,4) as 'MAGNETIC POTENTIAL'

  surface(Aphi) as 'MAGNETIC POTENTIAL' viewpoint (-1,1,30)

 

End

 


Page url: index.html?applications_magnetism_vector_magnet_coil.html