EEE340Lecture : Magnetic Circuits Analysis of magnetic circuits is based on Or where V m =NI is called a magnetomotive force (mmf) Also Or (6.83) (6.84) (6.82)

EEE340Lecture 242 Example 6-10: Determine magnetic flux density and and magnetic field density and for a toroidal core of permeability . Solution From Ampere’s law, (6.85) (6.86)

EEE340Lecture 243 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)

EEE340Lecture 244 where the reluctance (6.94)

EEE340Lecture 245 Magnetic circuitElectric circuit mmf, V m :=NI emf,  Flux,  Current, I Reluctance, RResistance, R Permeability,  Conductivity,  Kirchhoff’s 1 st Kirchhoff’s 2 nd

EEE340Lecture Boundary conditions for magnetostatic fields From i.e.  1 H 1n =  2 H 2n Normal components of B is continuous across an interface. From we can obtain (6.107) (T) (6.108) (6.111)

EEE340Lecture 247 Example 6-12: The two-layer magnetic media of permeability  1 and  2 are separated by a boundary. Show that Show. (6.114)

EEE340Lecture 248 Taking a ration of the two equations: I.e. The magnitude of H 2 (6.116) H1 H2

EEE340Lecture 249 Project: 1.You will solve the 2D Laplace equation numerically using iteration procedure, referred to as the relaxation method. 2.Upon your numerical results of the potential on the mesh, you need to draw the equal-potential lines as in the paper. 3.Draw the electric flux lines ( e-filed lines) as in the paper. 4.Compute the capacitance C: n a b y x