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Ampere’s Law is a relationship between:
• the magnetic field around a closed path, and
• the net current passing through an open surface bounded by the path.
sdB
enclosedi
enclosed0isdB
Ampere’s Law does not depend on the size and shape of the closed path, or of the surface bound by the path.
It also does not depend on the position of the current inside the path.
Like Gauss’ Law, we can use it to find the field in some situations with a high level of symmetry.
i
Magnetic field inside a cylindrical current-carrying conductor
r“Amperian loop”
R
B
rBsdB 2
2
2
enclosed R
rii
i
Magnetic field inside a cylindrical current-carrying conductor
r“Amperian loop”
R
B
rR
iB
20
2 (direction from
right-hand rule!)