6-8: Magnetic Circuits

1

• 6-8 Magnetic Circuits
• Analysis of magnetic circuits is based on
• Or
• where VmNI is called a magnetomotive force (mmf)
• Also
• Or
• Or

(6.83)
(6.84)
(6.82)
2

• Example 6-10 Determine magnetic flux density
  and and magnetic field density and
  for a toroidal core of permeability m.
• Solution
• From Amperes law,

(6.85)
(6.86)
3

• Substituting,
• The magnetic flux in the circuit is
  , where S is the cross-section area
  of the core.
• Combining (6.92) and (6.89), we have
• This equation can be cast in circuit model.

(6.89)
(6.92)
(6.93)
4

• where the reluctance

(6.94)
5

Magnetic circuit Electric circuit
mmf, VmNI emf, e
Flux, f Current, I
Reluctance, R Resistance, R
Permeability, m Conductivity, s

Kirchhoffs 1st
Kirchhoffs 2nd
6

• 6-10 Boundary conditions for magnetostatic fields
• From
• i.e. m1H1nm2H2n
• Normal components of B is continuous across an
  interface.
• From
• we can obtain

(6.107)
(T)
(6.108)
(6.111)
7

• Example 6-12 The two-layer magnetic media of
  permeability ?1 and ?2 are separated by a
  boundary. Show that
• Show.

(6.114)
8

• Taking a ration of the two equations
• I.e.
• The magnitude of H2

H1
H2
(6.116)
9

• Project
• You will solve the 2D Laplace equation
  numerically using iteration procedure, referred
  to as the relaxation method.
• Upon your numerical results of the potential on
  the mesh, you need to draw the equal-potential
  lines as in the paper.
• Draw the electric flux lines ( e-filed lines) as
  in the paper.
• Compute the capacitance C

y
b
x
n
a