Amperes Law Andre Marie Ampere 17751836

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Amperes Law Andre Marie Ampere (1775-1836)
Chapter 29 continued .
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Amperes Law
Enclosing a current carrying wire with a loop and
taking the dot product of B and ds along that
loop determines the amount of current enclosed by
the loop.
For geometries with a high degree of symmetry one
can determine the magnetic field from Amperes LAW
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Amperes Law
How do you use this equation to determine B?
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Examples of Current sources with a high degree of
symmetry

• Long Straight Wire
• Toroid
• Solenoid

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Long Straight Wire with a constant current
For rgtR, radius of wire the magnetic field must
have cylindrical symmetry
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Example

• Long Straight Wire

For r lt R the magnetic field must have
cylindrical symmetry and the current enclosed is
only part of I
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Example

• Long Straight Wire

Result of considering paths 1 and 2
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Sample Problem
What is the magnetic field at r3cm a2cm
b4cm Jcr2
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• Solenoid - A long cylinder with wire closely
  wrapped around it. The length is much larger than
  the diameter.

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• Ideal Solenoid

Constant field in x-direction
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Magnetic Field inside a donut (toroid) mmm
There is circular symmetry here, the field will
be constant along the circular path concentric
with the center axis of the toroid
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Example Problem 5

• What current must flow through the wires of a
  toroid to generate a 1.0 T magnetic field at its
  center (10 cm radius) if it has 500 turns of
  wire? etc ..