Physics 2102 Jonathan Dowling. Physics 2102 Lecture 16. Ampere’s law . André Marie Ampère (1775 – 1836). q. q. Flux=0!. Ampere’s law: Remember Gauss’ law?. Given an arbitrary closed surface, the electric flux through it is proportional to the charge enclosed by the surface.
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No isolated magnetic poles! The magnetic flux through any closed “Gaussian surface” will be ZERO. This is one of the four “Maxwell’s equations”.
dsAmpere’s law: a Second Gauss’ law.
The circulation of B
(the integral of B scalar
ds) along an imaginary
closed loop is proportional
to the net amount of current
traversing the loop.
Thumb rule for sign; ignore i4
As was the case for Gauss’ law, if you have a lot of symmetry,
knowing the circulation of B allows you to know B.
rAmpere’s Law: Example 2 (cont)
For r>R, ienc=i, so
For r < R
All loops in the figure have radius r or 2r. Which of these arrangements produce the largest magnetic field at the point indicated?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 m=NiA.
Since the coil curries a current, it produces a magnetic field, that can be calculated using Biot-Savart’s law:
Calculate the magnitude and direction of the resultant force acting on the loop.