Magnetic boundary conditions

1. Magnetic Boundary Conditions
Mr. HIMANSHU DIWKAR
Assistant professor
Department of ECE
Mr. Himanshu Diwakar, AP JETGI 1

2. Boundary Conditions
• Just as the electric field obeys certain rules, the magnetic field (H-field) also
obeys certain rules along the boundary of two different materials. And again, the
rules depend on whether we are discussing the tangential component (Ht) or the
normal/perpendicular component (Hn) to a surface.
• Now, just as there exists the parameter "permittivity" that is associated with
electric fields, there exists an analogous parameter for magnetic fields -
permeability, written by the symbol 𝜇
• This is a property of a material which basically describes how a material
concentrates magnetic fields. The units are measured in Henries/meter [H/m],
which is a measure of inductance over a length.
Mr. Himanshu Diwakar, AP JETGI 2

3. A Material Boundary, along with the Tangential and Perpendicular
Magnetic Fields.
Here we will have the normal
component of the magnetic
flux density (B) continuous
across a boundary.
Mr. Himanshu Diwakar, AP JETGI 3

4. • That is, the vector Bn1 (normal component of B immediately inside region 1) is
equal to the vector Bn2 (normal component of B immediately inside region 2).
• And since B and H are related by the permeability, we know how the normal
component of the magnetic field H changes across the boundary.
• Note that it doesn't matter what the conductivities (𝜎) or permittivities (𝜀) are in
the two regions - they don't affect the magnetic field's boundary conditions.
• For the tangential magnetic field (Ht) at a material discontinuity, it is a little more
tricky. Recall that magnetic fields are created due to electric current flowing.
• Hence, if no electric current is flowing on the surface (I=0), then the magnetic
field will be continuous across a material boundary change
Mr. Himanshu Diwakar, AP JETGI 4

5. • Suppose current is flowing on the
surface. Then this must give rise to it's
own magnetic field on the surface, thus
making the magnetic fields (Ht1 and
Ht2) discontinuous? Right you are.
• In that case, we write the surface current
as K, which has units of Amps/meter.
This is illustrated in Figure
A Boundary Between Two Materials, with a Surface Current
Flowing on the Boundary
Mr. Himanshu Diwakar, AP JETGI 5

6. • In this case, we will have the magnetic field discontinuous by the exact amount of
surface current
• states that the tangential component of the magnetic field will be discontinous by
the amount of surface current at the boundary (K). That is, Ht1 is the component
of the magnetic field tangnetial to the material boundary just inside the region 1.
This will differ from Ht2 (the tangential magnetic field just inside region 2) only if
an electric current flows on the surface
Mr. Himanshu Diwakar, AP JETGI 6

7. Inductors and inductances
• If a changing flux is linked with a coil of
a conductor there would be an emf
induced in it. The property of the coil of
inducing emf due to the changing flux
linked with it is known as inductance of
the coil.
• Due to this property all electrical coil can
be referred as inductor. In other way, an
inductor can be defined as an energy
storage device which stores energy in
form of magnetic field.
Mr. Himanshu Diwakar, AP JETGI 7

8. • A current through a conductor produces a magnetic field surround it.
The strength of this field depends upon the value of current passing
through the conductor.
• http://www.electrical4u.com/what-is-inductor-and-inductance-theory-of-inductor/
Mr. Himanshu Diwakar, AP JETGI 8

9. Definition of Self Inductance
• Whenever, current flows through a circuit or coil, flux is produced
surround it and this flux also links with the coil itself
• So, it can be concluded that self-induced emf is ultimately due to
changing current in the coil itself.
• And self inductance is the property of a coil or solenoid.
Mr. Himanshu Diwakar, AP JETGI 9

10. Explanation of Self Inductance of a Coil
• Whenever changing flux, links with a circuit, an emf is induced in the
circuit. This is Faraday’s laws of electromagnetic induction. According
to this law
• Where, e=induced emf
• N=number of turns
• (dφ/dt)=rate of change of flux leakage with respect to time.
• Unit of Inductance= Henry
• The negative sign of the equation indicates that the induced emf
opposes the change flux linkage
• This is according to Len’z law of induction.
Mr. Himanshu Diwakar, AP JETGI 10

11. Magnetic Energy.
• Magnetic energy is the energy within a magnetic field. This energy results in
various metals either repelling or attracting each other.
• Magnetic field can be of permanent magnet or electro-magnet. Both magnetic
fields store some energy.
• Permanent magnet always creates the magnetic flux and it does not vary upon the
other external factors. But electromagnet creates its variable magnetic fields based
on how much current it carries.
𝐸 =
1
2
𝐿𝐼2
Mr. Himanshu Diwakar, AP JETGI 11

12. Thank you
Questions?
Mr. Himanshu Diwakar, AP JETGI 12