Physics 2102 Jonathan Dowling Lecture 21 FRI 06 MAR Magnetic fields Ch 28 8 10 28 8 Force on Current in Wire 28 9 Torque on Current Loop 28 10 Magnetic Dipole Moment Magnetic Force on a Wire L F iL B dF i dL B Magnetic Force on a Straight Wire in a Uniform Magnetic Field If we assume the more general case for which the magnetic field B forms an angle with the wire the magnetic force equation can be written in vector form as FB iL B Here L is a vector whose 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 s in B i dF dFB idL B FB i dL B dL Magnetic Force on a Wire of Arbitrary Shape Placed in a 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 dFB idL B The net magnetic force on the 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 iabB sin 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 NiA n n Right hand rule curl fingers in direction of current thumb points along B As in the case of electric dipoles magnetic dipoles tend to align with the magnetic field Electric vs Magnetic Dipoles NiA n Q p Qa Q QE E p E UE p E QE B B U B B DC Electric Motor
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