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Amperes Law Andre Marie Ampere 17751836

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... a high degree of symmetry one can determine the magnetic field from Ampere's LAW. Ampere's Law ... sources with a high degree of symmetry. Long Straight ... – PowerPoint PPT presentation

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Title: Amperes Law Andre Marie Ampere 17751836


1
Amperes Law Andre Marie Ampere (1775-1836)
Chapter 29 continued .
2
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
3
Amperes Law
How do you use this equation to determine B?
4
Examples of Current sources with a high degree of
symmetry
  • Long Straight Wire
  • Toroid
  • Solenoid

5
Long Straight Wire with a constant current
For rgtR, radius of wire the magnetic field must
have cylindrical symmetry
6
Example
  • Long Straight Wire

For r lt R the magnetic field must have
cylindrical symmetry and the current enclosed is
only part of I
7
Example
  • Long Straight Wire

Result of considering paths 1 and 2
8
Sample Problem
What is the magnetic field at r3cm a2cm
b4cm Jcr2
9
  • Solenoid - A long cylinder with wire closely
    wrapped around it. The length is much larger than
    the diameter.

10
  • Ideal Solenoid

Constant field in x-direction
11
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
12
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 ..
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