JETGI 1

Magnetic Boundary Conditions

Mr. HIMANSHU DIWKARAssistant professor

Department of ECE

Mr. Himanshu Diwakar, AP

JETGI 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 

• 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 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 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 () or permittivities () 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 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 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 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 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 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 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 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.

Mr. Himanshu Diwakar, AP

JETGI 12

Thank youQuestions?

Mr. Himanshu Diwakar, AP