![]() Consult a text such as Jiles for details oncorrecting for demagnetizing fields. Demagnetizing fields only have exact analytical solutions forspheroidally shaped specimens. For them the internal 'demagnetizing field'leads to lower values of force than equation FRL would suggest. It needsemphasizing that this formula will give significant overestimates forferromagnetic materials. Where l is distance and v is the volume of the material. This is thebasis of one solution to the problem: It will say that its inductance is changing. Theelectromagnet you are using will have an opinion about changes to thefield it generates. So for there to be a force on a piece of iron then a displacement ofthe iron must result in an alteration to the field energy. The filings tend to line upwith the field but don't generally move much because they are so small thatthe field appears uniform to them. Think about the famous experiment with iron filings sprinkledonto a piece of cardboard above a bar magnet. Note that we still don't havea translational force (provided that the field is uniform on the scale ofthe rod). When the rod is aligned with the field the flux can gofurther through a high permeability region. Flux goes easier through high permeability thanthrough low. Think of current flow through aresistor the current has an easier time going through a low resistancethan a high resistance. Equation EFB has μ on the denominator so the fieldenergy is lower here than in the air, and the further the flux can gothrough the iron the lower the energy. The fluxlines prefer the iron to the air because of the higher permeability. What happens is that the axis of the rod will bedrawn into alignment with the field - like a compass needle. ![]() This is different becausewe've lost symmetry. OK, instead of the sphere let's try an iron rod. If there is translational movement then allthat can happen if the sphere were to move is that the distortion of thefield around the original position of the sphere will disappear and thesame distortion will be re-established around the new position thetotal system energy will remain unchanged. A sphere has perfect symmetry, so rotation will notchange the picture in any way. Now, the point is that there will be no net force on the iron, no matterhow strong the field. Inside the ironthe lines will be quite concentrated (though parallel to the originalfield). ![]() The flux lines will bend in thevicinity of the iron so that they will converge upon it. Take aninitially uniform magnetic field in free space and introduce into it aniron sphere. We assume thatthe core is initially unmagnetized and that the electrical energy (W)supplied to the coil will all be converted to magnetic field energy inthe core (we ignore eddy currents).Ĭompare this result with the better known formula for the energy stored by a given inductance, L:Ī 'hand-waving' explanation might help clarify the physics. We let the flux pathlength around the core be equal to L f and thecross-sectional area be equal to A x. We choose a toroid because over its cross-sectional area, A, the fluxdensity should be approximately uniform (particularly if the coreradius is large compared with it's cross section). It's the power needed to push the current intothe coil against this voltage which we now calculate. The increase in flux induces avoltage in the coil. That, in turn, leads to an increase in magnetic flux. When the coil current increases so does the magneticfield strength, H. ![]() We equate thefield energy to the electrical energy needed to establish the coilcurrent. To derive an expression for the field energy we'll look at thebehaviour of the field within a simple toroidal inductor. One method of calculating the force produced by a magnetic field involvesan understanding of the way in which the energy represented by the fieldchanges. Although the answers are elusive this page outlines somegeneral principles and pointers towards specific solutions.Ībout your browser: if this character '×' does not look like amultiplication sign, or you see lots of question marks '?' or symbolslike ' ' or sequences like '&cannot ' then please accept my apologies. You're designing an electromagnet, for example, and need to calculatethe number of turns, or you might already have a coil and want to knowhow hard it will pull on a nearby piece of iron. The force produced by a magnetic field The force produced by a magnetic field
0 Comments
Leave a Reply. |