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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André Marie Ampère
(1775 – 1836)
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.
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.
direction as B field lines!)
RAmpere’s Law: Example 2
Current into page, circular field lines
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.