Lecture 21: FRI 06 MARPowerPoint PresentationSlide 3Slide 4Magnetic Dipole MomentElectric vs. Magnetic DipolesSlide 7Lecture 21: FRI 06 MAR Lecture 21: FRI 06 MAR Magnetic fields Magnetic fields Ch.28.8-10 Physics 2102Jonathan Dowling28.8 Force on Current in Wire28.9 Torque on Current Loop28.10 Magnetic Dipole MomentQuickTime™ and a decompressorare needed to see this picture.Magnetic Force on a Wire.Magnetic Force on a Wire.LBLiFrrr×=BLiFrrr×=BLdiFdrrr×=BLdiFdrrr×=.dLrBrdFriφIf we assume the more general case for which themagnetic field forms an angle with the wirethe magnetic force equation can be writtenB φMagnetic Force on a Straight Wire in a Uniform Magnetic Field r in vectorform as . Here is a vector whose magnitude is equal to the wire length and has a direction that coincides with that of the current.The magnetic force magnitude is sBBF iL B LLF iLB= ×=r r r rin .In this case we divide the wire into elements oflength , which can be considered as straight.The magnetic force dLφMagnetic Force on a Wire of Arbitrary ShapePlaced in a Nonuniform Magnetic Field on each element is. The net magnetic force on the wire is given by the integral .BBdF idL BF i dL B×= ×∫= r r rr r rBF iL B= ×r r rBdF idL B×=r r r BF i dL B= ×∫r r r(28-12)Torque on a Current Loop:Principle behind electric motors.Net force on current loop = 0iaBFF ==31)sin(1θFF =⊥)sin(θτ iabBbFTorque ===⊥For a coil with N turns,=N IABsin, where A is the area of coilRectangular coil: A=ab, current =iBut: Net torque is NOT zero!nNiAˆ)(=μrnˆ,μrMagnetic Dipole MomentMagnetic Dipole MomentN=number of turns in coilA=area of coil.We just showed: =NiABsinRight hand rule:curl fingers in direction of current; thumb points along Define: magnetic dipole moment Brrr×=μτAs in the case of electric dipoles, magnetic dipoles tend to align with the magnetic field.Electric vs. Magnetic DipolesElectric vs. Magnetic Dipoles € UE= −r p ⋅r E -QQEQE+Qp=Qa € r τ B=r μ ×r B nNiAˆ)(=μr € r τ E=r p ×r E € UB= −r μ ⋅r BDC Electric
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