University Physics Notes: Electricity and Electromagnetism - Using Ampere's Law to Find The Magnetic Field in a Conductor with a Uniform Current Density
The above conductor has circular cross section of radius R and
carries a current I, so the current density is
The area enclosed by the circular loop is
so
the current enclosed within the loop
is
Around the loop
the
field
is
uniform by symmetry.
Applying Ampere's Law:
Dividing by
gives