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Electricity & Magnetism. Seb Oliver Lecture 14: Biot-Savart Law. Summary: Lecture 13. Practical uses of moving charge in magnetic field Lorentz Force Force on Wire. Biot-Savart Law. Introduction.

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electricity magnetism

Electricity & Magnetism

Seb Oliver

Lecture 14:

Biot-Savart Law

summary lecture 13
Summary: Lecture 13
  • Practical uses of moving charge in magnetic field
  • Lorentz Force
  • Force on Wire
introduction
Introduction
  • We have discussed how an existing magnetic field influences moving charges (and thus currents)
  • We have not yet discussed the origin of magnetic fields
  • We will now see that currents (moving charges) produce magnetic fields
  • This can be thought of as the basic mechanism by which all magnetic fields are produced
history
History
  • 1819 Hans Christian Oersted discovered that a compass needle was deflected by a current carrying wire
  • Then in 1920s Jean-Baptiste Biot and Felix Savart performed experiements to determine the force exerted on a compass by a current carrying wire
  • There results were as follows …
jean baptiste biot felix savart s results
Jean-Baptiste Biot & Felix Savart’s Results
  • dB the magnetic field produced by a small section of wire
  • ds a vector the length of the small section of wire in the direction of the current
  • r the positional vector from the section of wire to where the magnetic field is measured
  • I the current in the wire
  • angle between ds & r

dB

r

ds

biot savart s results
Biot & Savart’s Results
  • dB perpendicular to ds
  • dB perpendicular to r
  • |dB| inversely proportional to |r|2
  • |dB| proportional to current I
  • |dB| proportional to |ds|
  • |dB| proportional to sin q
biot savart law1
Biot – Savart Law
  • All these results could be summarised by one “Law”

Putting in the constant

Where m0 is the permeablity of free space

magnetic field from biot savart law

dB2

dBi

ri

dsi

r2

ds2

Magnetic Field from Biot-Savart Law
  • We can use the Biot-Savart law to calculate the magnetic field due to any current carrying wire
  • B = dB1+dB2+…+dBi
  • I.e. B =SdB

dB1

r1

ds1

one example of using the biot savart law

One Example of using the Biot-Savart Law

Direction of the field around a long wire

magnetic field from biot savart law1

dB

r

ds

Magnetic Field from Biot-Savart Law
  • We can use the Biot-Savart law to see the direction of the field due to a wire segment

dB1

dB1

r1

r1

ds1

magnetic field from biot savart law2
Magnetic Field from Biot-Savart Law

dB1

r1

c.f.

Of course there is no such thing as an isolated current segment!

summary
Summary
  • Biot-Savart Law
    • (Field produced by wires)
    • Centre of a wire loop radius R
    • Centre of a tight Wire Coil with N turns
    • Distance a from long straight wire
  • Force between two wires
  • Definition of Ampere