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Biot-Savart Law

A presentation for class XII

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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

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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 …

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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
  • θ angle between ds & r

r

ds

dB

θ

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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 θ

​

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Biot – Savart Law

  • All these results could be summarised by one “Law”

Putting in the constant

Where μ0 is the permeablity of free space

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Magnetic Field from Biot-Savart Law

  • B = dB1+dB2+…+dBi
  • I.e. B =ΣdB

r1

ds1

dB1

r2

ds2

dsi

dBi

ri

dB2

  • We can use the Biot-Savart law to calculate the magnetic field due to any current carrying wire

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One Example of using the Biot-Savart Law

Direction of the field around a long wire

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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

r1

ds1

dB1

dB1

r1

ds

r

dB

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Another Right-Hand Rule

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Magnetic Field from Biot-Savart Law

dB1

r1

c.f.

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

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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