Summary of magnetostatics

1
Summary of magnetostatics

• for dc currents, in the absence of permanent
  magnets, summarizing everything we have so far

2
Magnetic materials

• in a manner very similar to dielectrics, bound
  currents can be induced in some materials
• these materials are not as common as
  dielectrics
• net result is the constitutive equation
• mo is the permeability of free space, 4px10-7
  henrys/meter
• mr is the relative permeability of the material
• ?m is the magnetic susceptibility
• unlike dielectrics, where the induced electric
  field always opposes the applied electric field,
  the induced magnetic field can either oppose or
  align with the applied field!
• the magnetic susceptibility can be positive or
  negative
• the relative permeability can be greater than or
  less than 1
• references
• http//www.ee.surrey.ac.uk/Workshop/advice/coils/m
  u/ferri
• http//hyperphysics.phy-astr.gsu.edu/hbase/solids/
  ferro.html

3
Classification of magnetic materials

• the different flavors of magnetic materials
  broadly fall into the following categories

4
materials

• note that ? can be either positive or negative
• the relation between B and H can get even more
  complicated

5
Magnetization or B-H curves

• in linear materials B and H and strictly
  proportional
• but in some materialsthe B field does not
  remain linearly related to the H field

adapted from http//www.ee.surrey.ac.uk/Workshop/a
dvice/coils/mu/ferri
6
Hysteresis

• in ferromagnetic materials you may well have a
  permanent magnetic effect
• the relation between B and H is not linear, and a
  memory effect (hysteresis) may be present

from http//www.ee.surrey.ac.uk/Workshop/advice/c
oils/mu/
7
Material examples

• adapted from http//www.ee.surrey.ac.uk/Workshop/a
  dvice/coils/mu/ferri

8
Magnetostatic boundary conditions

• for many materials the relative permeability is
  very close to 1
• nothing to worry about here, just use mo
  everywhere
• for the cases where mr is not one, we have BCs
  very similar to what we had for dielectrics
• method of derivation also looks similar, using
  Biot-Sarvat law and Amperes law this time
• at the interface between two magnetic materials
• the component of the B field normal to the
  interface between the two materials is continuous
  (use Biot-Sarvat law to get this one)
• the component of the H field tangent to the
  interface is equal to the surface current density
  at the interface (use Amperes law to get this
  one)
• if theres no current, Htan is continuous

9
Summary of magnetostatics

• for dc currents, in the absence of permanent
  magnets, summarizing everything we have so far

• whats next?
• magnetic coupling and inductance.