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PHY110W MAGNETISM <strong>MAGNETIC</strong> <strong>FIELDS</strong> <strong>DUE</strong> <strong>TO</strong> <strong>CURRENTS</strong><br />
FORCE BETWEEN<br />
TWO PARALLEL CONDUC<strong>TO</strong>RS<br />
d<br />
B L<br />
F a<br />
b<br />
ba<br />
F <br />
ab<br />
B <br />
a<br />
i a<br />
i b<br />
b<br />
The magnitude of the magnetic field due to the current<br />
in wire a at every point on wire b is given by<br />
B<br />
a<br />
µ 0ia<br />
=<br />
2π<br />
d<br />
and consequently the magnitude of the force on wire b<br />
due to the magnetic field of wire a (written F ba ) is<br />
µ 0Liaib<br />
Fba = iLB b a = = Fab<br />
(30-15)<br />
2π<br />
d<br />
• F ba and F ab are an action-reaction pair.<br />
• Parallel currents attract.<br />
• Antiparallel currents repel.<br />
The ampere can now be defined as …<br />
that unvarying current which, when maintained in each<br />
of two parallel conductors of infinite length and situated<br />
one metre apart in empty space, causes between them a<br />
force of exactly 2 × 10 -7 N per metre of length.<br />
19
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