Magnetic Field

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Magnetic field description along with Maxwell's equation

Text of Magnetic Field

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Magnetic FieldSubject : Electromagnetics Theory Introduction Definition A magnetic field is the magnetic effect of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude as such it is a vector field.Denoted by : B or HUnit : Am1or A/m or teslas (T)

understandingWhenever electron moves Magnetic Field is generated associated with movement.Now we are very well aware of magnetic field created by electric currents. We can easily relate previous statement with this phenomenon. However, magnetic field of permanent magnets can create confusion with that statement. In permanent magnets, examining on atomic level we can notice the movement of electrons with magnetic moments in one direction causing magnetic field. In non magnetic fields magnetic moments of electrons in every orbit is canceled by each other. Iron has two electrons that can be aligned, so it is the "strongest" magnetic material.Magnetic filed lines A pictorial representation of magnetic field lines is very useful in visualizing the strength and direction of the magnetic field . The direction of magnetic field lines is defined to be the direction in which the north end of a compass needle points.There are many types of magnets differing by shape creating different patterns of magnetic filed lines as below :

Magnetic field by Bar magnet Magnetic field by Horseshoe magnet Magnetic field by Horseshoe magnet Toroidal Magnetic FieldPropertiesThey seek the path of least resistance between opposite magnetic poles. In a single bar magnet as shown to the right, they attempt to form closed loops from pole to pole.They never cross one another.They all have the same strength.Their density decreases (they spread out) when they move from an area of higher permeability to an area of lower permeability.Their density decreases with increasing distance from the poles.They are considered to have direction as if flowing, though no actual movement occurs.They flow from the south pole to the north pole within a material and north pole to south pole in air.differentiating B and H It's all to do with the difference between free charge and bound charge (which together make total charge). E and B are the total electric and magnetic fields. D and H are the free electric and magnetic fields. P and M are the bound electric and magnetic fields. So E = D + P (except that for historical reasons E is defined differently, so we need to multiply it by the permittivity, and for some reason P is multiplied by minus-one ). And B = H + M (except that for the same historical reasons B is defined like E, so we need to divide it by the permeability). The latter equation says that the total magnetic field equals the free magnetic field plus the bound magnetic field (the bound magnetic field is all those little loopy currents that make things magnetic). When an electric current produces a magnetic field, it couldn't care what the field is going to be used for (i.e. for bold sweeping field lines or pokey little loops inside matter), so it produces a total field, which it's sensible to measure as B. But once we put matter in the way, we can only measure the free field, H.Basically, (apart from the permeability factor, of course) B and H are the same away from matter, but in or near matter the matter soaks up some of the B, and all we measure is what's left, the H.differentiating B and H (cont.) Based on Maxwell's equations, electric fields are generated by changing B fields, while H fields are generated by changing electric fields. In dc fields, static electric E fields create currents (magnetization currents) I which in turn produce static H fields. A static B field cannot produce an electric field E. Even if we used natural units where 0 = 0 = 1, this distinction between B and H remains. In magnetic materials, B is not linearly related to H due to the magnetization term M. B = H in space, then B H in magnetic materials. If voltage = d/dt Bn dA, then how can curl H= E = voltage/length if B = H? So even if 0 = 0 = 1, they have to have units.

Important note : Magnetic Field term is historically assigned to symbol H and B to all other terms. But generally in many books it is also used for B as well and also used usually by physicists and professors. BIOT-SAVART'S LAW

BIOT-SAVART'S LAW (cont.)

AMPERE'S CIRCUIT LAW - MAXWELL'S EQUATIONMAGNETIC FLUX DENSITY - MAXWELL'S EQUATION

MAGNETIC FLUX DENSITY - MAXWELL'S EQUATION

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