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Chapter 30

PHYSICS 1E03 Chapter 30: Sources of Magnetic Field

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McMaster University
David Chettle

Chapter 30: Sources of the Magnetic Field  Biot-Savart Law o Experiments on the force exerted by an electric current on a nearby magnet o The expression is based on the following observations for the magnetic field dB at a point P associated with a length element ds of wire carrying steady current I  The vector dB is perpendicular both to ds (which points in the direction of current) and to the unit vector r directed from ds toward P  The magnitude of dB is inversely proportional to r where r is the distance from ds to P  The magnitude of dB is proportional to the current I and to the magnitude ds of the length element ds  The magnitude of dB is proportional to sin θ, where θ is the angle between the vectors ds and r o o Valid for current consisting of charges flowing through space (in this case, ds represents the length of a small segment of space in which the charges flow o A current element must be part of an extended current distribution because a complete circuit is needed for charges to flow o Note that here, the magnetic field at O due to the current in the straight segments AA’ and CC’ is zero because ds is parallel to r along these paths, which means that ds X r = 0 for these paths o Because we can ignore these segments, the application of the Biot-Savart law only applies to the curved wire segment AC o The equation we are left with: o The magnetic field is into the page at O  What about around a circle current loop? o The field vector can be resolved into components: dBxand dBPerp o The perpendicular components, because of the symmetry of the ring, cancel. o All length elements are at the 2 2 2 same distance r from P: where r = a + x o We are left with: o  Magnetic Force between two parallel Conductors o The magnitude of B 2e already know, so the equation of the force becomes: F 1 o Parallel conductors carrying currents in the same direction attract each other, parallel conductors carrying currents in the opposite directions repel each other o Force between these two parallel wires is used to define the ampere:  When the magnitude of the force per unit length between two long, parallel wires that carry identical currents and are separated by 1 m is
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