Electricity

1
Electricity Magnetism

• Seb Oliver
• Lecture 14
• Biot-Savart Law

2
Summary Lecture 13

• Practical uses of moving charge in magnetic field
• Lorentz Force
• Force on Wire

3
Biot-Savart Law
4
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

5
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 Savarts 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
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Biot Savarts Results

• dB perpendicular to ds
• dB perpendicular to r
• dB inversely proportional to r2
• dB proportional to current I
• dB proportional to ds
• dB proportional to sin q

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Biot Savart Law

• All these results could be summarised by one Law

Putting in the constant
Where m0 is the permeablity of free space
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Magnetic Field from Biot-Savart Law

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

dB1

• B dB1dB2dBi
• I.e. B SdB

r1
ds1
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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

dB1
dB1
r1
r1
ds1
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Another Right-Hand Rule
13
Magnetic Field from Biot-Savart Law
dB1
r1
c.f.
Of course there is no such thing as an isolated
current segment!
14
Summary Lectures 14 15

• 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