Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Time in physics wikipedia , lookup
Electrostatics wikipedia , lookup
Field (physics) wikipedia , lookup
History of electromagnetic theory wikipedia , lookup
Condensed matter physics wikipedia , lookup
Maxwell's equations wikipedia , lookup
Neutron magnetic moment wikipedia , lookup
Magnetic field wikipedia , lookup
Magnetic monopole wikipedia , lookup
Electromagnetism wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Superconductivity wikipedia , lookup
Lecture 8 MAGNETOSTATICS Magnetic Fields Fundamental Postulates of Magnetostatics in Free Space Prof. Viviana Vladutescu Magnetic Fields Magnetism and electricity have not been considered distinct phenomena until Hans Christian Oersted conducted an experiment that showed a compass deflecting in proximity to a current carrying wire Produced by -time varying electric fields -permanent magnet (arises from quantum mechanical electron spin/ can be considered charge in motion=current ) -steady electric currents H SI A m If we place a wire with current I in the presence of a magnetic field, the charges in the conductor experience another force Fm Fm ~ q, u, B H 1 B q –charge u –velocity vector B -strength of the field (magnetic flux density) μr –relative permeability μ –absolute permeability 7 μ0-permeability of the free space 0 4 10 ( H ) M=χmH- is the magnetization for linear and homogeneous medium Relative permeabilities for a variety of materials Material μ/(H m-1) μr Application Ferrite U 60 1.00E-05 8 UHF chokes Ferrite M33 9.42E-04 750 Resonant circuit RM cores Nickel (99% pure) 7.54E-04 600 - Ferrite N41 3.77E-03 3000 Power circuits Iron (99.8% pure) 6.28E-03 5000 - Ferrite T38 1.26E-02 10000 Broadband transformers Silicon GO steel 5.03E-02 40000 Dynamos, mains transformers supermalloy 1.26 1000000 Recording heads Lorentz’s Force equation Fe q E Fm qu B Fe Fm F F q( E u B) Note: Magnetic force is zero for q moving in the direction of the magnetic field (sin0=0) When electric current is passed through a magnetic field a force is exerted on the wire normal to both the magnetic field and the current direction. This force is actually acting on the individual charges moving in the conductor. The magnetic force is exerting a torque on the current carrying coil r Fm r Fm sin an Cross product Fundamental Postulates of Magnetostatics in Free Space B 0 B 0 J J 0 Law of conservation of magnetic flux B d s 0 s There are no magnetic flow sources, and the magnetic flux lines always close upon themselves Ampere’s circuital law B d s J d s 0 s s B d l I 0 c The circulation of the magnetic flux density in free space around any closed path is equal to μ0 times the total current flowing through the surface bounded by the path Stoke’s Theorem H d s H d l s c Note: For a closed surface there will be no surface bounding external contour Proof: Sum over H s a j where H lim s 0 n H d l c s Note: The net contribution of all the common parts in the interior to the total line integral is 0 and only the contribution from the external contour C remains after summation lim H d l H d l s j 0 j 1 c c N H ds H d l s c The maximum circulation of H per unit area as the area shrinks to zero is equal to the current density through that area Jds H d l c H d l I enc c Two possible Amperian paths around an infinite length line of current. Postulates of Magnetostatics in Free Space Differential Form B 0 B 0 J Integral Form B d s 0 s B d l I 0 c Example Given a 3.0 mm radius solid wire centered on the z-axis with an evenly distributed 2.0 amps of current in the +az direction, plot the magnetic field intensity H versus radial distance from the z-axis over the range 0 ≤ r ≤ 9 mm. The field from a particular line of current making up the distributed current The field from a second line of current results in the cancellation of ar component H dL I enc , where H H a and dL r d a ; This will be true for each Amperian path. I AP1: I enc J dS, J = a 2 a z , I enc I H r a for r a 2 2 a AP2: Ienc = I, H I 2r a for r a r 2r H I enc 2 I Ir 2 2 r d r d 2 a 0 a 0