Physics 2102 Jonathan Dowling Lecture 21 FRI 06 MAR Magnetic fields Ch 28 8 10 28 8 Force on Current in Wire QuickTime and a decompressor are needed to see this picture 28 9 Torque on Current Loop 28 10 Magnetic Dipole Moment Magnetic Force on a Wire L r r r F i L B r r r dF i dL B Magnetic ForceonaStraight Wireina Uniform Magnetic Field If we assume the more general case for which the r magnetic field B forms an angle with the wire the magnetic force equation can be written in vector r r r r form as FB iL B Here L is a vector whose r r r FB iL B magnitude is equal to the wire length L and has a direction that coincides with that of the current The magnetic force magnitude is FB iLB sin r B i r dF r r r dFB idL B r r r FB i dL B r dL Magnetic Forceona Wireof Arbitrary Shape Placed ina Nonuniform Magnetic Field In this case we divide the wire into elements of length dL which can be considered as straight The magnetic force on each element is r r r dFB idL B The net magnetic force on the r r r wire is given by the integral FB i dL B 28 12 Principle behind electric motors Torque on a Current Loop Rectangular coil A ab current i Net force on current loop 0 But Net torque is NOT zero F1 F3 iaB F F1 sin Torque F b iabBsin For a coil with N turns N I A B sin where A is the area of coil Magnetic Dipole Moment We just showed NiABsin N number of turns in coil A area of coil Define magnetic dipole moment r NiA n r n Right hand rule curl fingers in direction of current thumb points along r r r B As in the case of electric dipoles magnetic dipoles tend to align with the magnetic field Electric vs Magnetic Dipoles r NiA n Q p Qa Q QE r r r E p E r r UE p E QE r r r B Br r U B B DC Electric Motor
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