Physics II chapter 28 notes

# Physics II chapter - Chapter 28 Sources of Magnetic Field In this chapter examine the source of magnetic fields magnetic charges(monopoles do not

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Chapter 28: Sources of Magnetic Field In this chapter… examine the source of magnetic fields magnetic charges (monopoles) do not exist, so what creates B field? in 1820, Oersted’s discovery: moving charge (current) creates B microscopic current loops (or “spin”) in bar magnets are source of magnetic field determining the magnetic field by the Biot-Savart law and Ampere’s law magnetic materials (diamagnetism, paramagnetism, ferromagnetism) Magnetic Field of a Moving Charge (28-1) B field of a moving charge q is proportional to q and falls off as 2 1/ r where r is distance away from charge v6.01 RS/BQ F’10 88 but direction of B is not radial: field at displacement r , points in direction of   ˆ qv r another right-hand rule: thumb points along v of positive charge, then fingers show sense in which field ‘wraps around’ for a point charge moving with constant velocity v , the magnetic field at location r with respect to the charge is Magnitude falls off as 1/r 2 in any given direction another fundamental constant: m / A 7 0 41 0 T   (exact!) , called the “permeability of free space” (Note: The letter “ ” does not designate “magnetic moment” here!) a deep connection: where c is the speed of light in vacuum   0 2 ˆ 4 qv r B r q v 1 r 2 r 3 r 4 r 1 B 2 B 3 B 4 B v B 00 1 c 

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example: attractive magnetic force between two like charges in parallel motion v6.01 RS/BQ F’10 89 example: perpendicular motion note that mag 21 F , and that the forces are neither repulsive nor attractive. What about Newton’s 3 rd law?. .. mag 12 F   Magnetic Field of a Current Element (28-2) magnetic field satisfies principle of superposition magnetic field of current element is sum of fields from charge carriers define d l to point along I current element with cross-sectional area A and infinitesimal length d l ( d l defines positive current direction) for n moving charges per unit volume, charge inside current element d l and current density d dQ qnA J nqv for average drift velocity d v , magnetic field at location r with respect to current element is for a complete circuit 2 q v 1 q v a y x   2 1 mag 00 21 22 2 mag 2 11 2 ˆˆ ˆ 44 ˆ qvi j v Fq v i q q aa qv i j v v i q q        due to1,at 2 due to2,at 1 2 2 2 ˆ ˆ j j   1 mag 0 2 2 2 mag 2 1 2 ˆ 0 4 ˆ qvj j v i a v v j q q due to1,at 2 due to 2,at 1 1 2 2 ˆ i 2 q v 1 q v B a y F x I d dB r l 0 0 2 ˆ 4 4 dd dQ v r qnA d v r 2 ˆ A dJ r Id dB rr r r r   l ll B r 0 2 ˆ 4 C r B r l I d l I (Biot - Savart law) I
Example: finding the magnetic field at center of semicircular loop:

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## This note was uploaded on 08/25/2011 for the course PHYSICS II 33-107 taught by Professor B.quinn during the Summer '10 term at Carnegie Mellon.

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Physics II chapter - Chapter 28 Sources of Magnetic Field In this chapter examine the source of magnetic fields magnetic charges(monopoles do not

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