# Physics 2102 Spring 2002 Lecture 8

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```					                                    Physics 2102

Jonathan Dowling

Lecture 24: FRI 13 MAR
Ch.29.5–6: Ampere’s Law

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decompressor
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André Marie Ampère
(1775 – 1836)
Ampere’s law: Closed
Loops
r
 B
—  ds  0ienclosed
LOOP

The circulation of B
(the integral of B scalar
ds) along an imaginary
r r
closed loop is
proportional to the net           B  d s  0 (i1  i2 )
amount of current              loop
traversing the loop.
Thumb rule for sign; ignore i3

If you have a lot of symmetry, knowing the circulation of B

allows you to know B.
Calculation of ienc . We curl the fingers
of the right hand in the direction in which
the Amperian loop was traversed. We note
the direction of the thumb.

All currents inside the loop parallel to the thumb are counted as positive.
All currents inside the loop antiparallel to the thumb are counted as negative.
All currents outside the loop are not counted.
In this example : ienc  i1  i2 .
Solenoids

B  0in
n  N /L  # Turns Per Unit Length
are need ed to see this p icture .
Magnetic Field in a Toroid “Doughnut” Solenoid

0 Ni
B
2r

                      QuickTime™ and a
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Toriod Fusion Reactor:
Power NYC For a Day on a Glass of H2O
Magnetic Field of a Magnetic Dipole
A circular loop or a coil currying electrical current is a
magnetic dipole, with magnetic dipole moment of
magnitude =NiA. Since the coil curries a current, it
produces a magnetic field, that can be calculated using
Biot-Savart’s law:
              
        0                0 
B( z )                   
2 ( R  z )
2   2 3/ 2
2 z 3
All loops in the figure have radius r or 2r. Which of
these arrangements produce the largest magnetic
field at the point indicated?
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Anima tion d ecompressor
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Neutron Star a Large Magnetic Dipole

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