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Chapter 30

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McMaster University

Physics

PHYSICS 1E03

David Chettle

Winter

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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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