Chapter 30 Sources of Magnetic Fields

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Chapter 30 Sources of Magnetic Fields

• PHYS 2326-18

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Concepts to Know

• Earths Field
• Magnetic Declination / Inclination
• 10 deg E of N declination here, inclination is
  up / down from horizontal
• Magnetic flux
• Gausss law for magnetism

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Concepts to Know

• Magnetic Field Of Moving Charge
• Permeability Constant
• Biot Savart Law
• Magnetic Field of a long straight wire
• Right Hand Rule

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Biot-Savart Law

• dB perpendicular to ds and to r where ds points
  in the direction of current I and r is the vector
  from the current element to P
• dB magnitude inversely proportional to r2 and
  proportional to current and magnitude ds and to
  the sine of ?, the angle between ds and r

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Permeability of Free Space

• The constant µo in Biot-Savart is called the
  permeability of free space.
• µo 4p 1.0E-7 T m /A Tesla meters /amp.
• µo 1.2566 E-6 Wb/A m where Wb is a weber or
  Tesla meter2 (magnetic flux)
• Note too that the speed of light c is related
• c2 1/(µo eo ) the permeability and
  permitivity of free space

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Finding B

• Note that Biot-Savart shows a differential dB
  rather than the total B at a point P
• To find B one must integrate over the current
  distribution
• Note that the integrand is a vector

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Magnetic field of Long Straight Wire

• See and go through Example 30.1
• Include eqn 30.5 on your next note card

P
?2
?1
a
I
O
x
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Current Right Hand Rule

• Grasp wire with thumb pointed in current flow
  direction.
• Fingers are wrapped around in direction of B
  which tends to be circular and with a magnitude
  at radius a from the wire given by eqn 30.5

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Field of Circular Coil

• Given a current loop of radius a at a distance x
  from the loop on the center axis find the B field
• by symmetry B will along the x axis

dB-
dB
ds
I
r
a
x
x
P
dBx
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Circular Coil

• See Example 30.3
• Also note for a solenoid of multiple turns N that
  these multiply by N since that multiples I

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Magnetic FluxGausss Law in Magnetism

• Electric flux is similar definition to magnetic
  field flux
• There is no magnetic monopole so no enclosed
  magnetic charge can be inside

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Magnetic Field of a Moving Charge

• A moving charge creates a magnetic field in the
  same fashion a current element creates a charge
  except that differential current element is part
  of a whole while a moving charge is the whole
  contribution

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Biot Savart Compared to Moving Particle

• Note the similarity between Biot Savarts current
  law and this moving particle
• I is charge per time moving past a point,
  velocity is distance per time
• For a point charge, dB becomes the whole field B

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Example 1

• Two protons moving together along the x-axis
  separated by 1mm in the y axis with a velocity
  v1.00 E7 m/s
• a) find the electric force between them
• b) find the magnetic force between them
• c) find the total force
• d) what happens if v 100 m/s

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Example 1

• Electric field Fe qE
• E k q/r2 1.439 E-3 N/C (a)
• Fe 2.3E-22 N repulsive
• B µo /4p q v/r2 1.6E-13
• Fb qvB 1.6 E-13 N/Am attractive (b)
• F Fe Fb 2.3E-22 N repulsive (c)
• Ratio Fe/Fb 899

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Example 1

• If velocity reduces, E field unchanged, B field
  changes, Fb changes
• B 1.6E-18 N/Am
• Fb 2.56E-34 N attractive
• F 2.3E-22N repulsive
• R Fe/Fb 8.99 E11

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Example 2

• Given a rectangular loop of 10cm x 20cm (a by b)
  with counter clockwise current I2A what is the
  magnitude and direction of magnetic field at the
  center point P
• B direction right hand rule out of page
• B BabBbcBcdBda 2Bab 2Bbc

a
d
I
P
b
c
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Example 2

• B 1.79E-5 T