University Physics Notes: Electricity and Electromagnetism – Using Ampere's Law to Find the Magnetic Field Inside a Long Solenoid
If we assume the solenoid to be long, then we can assume the
magnetic field inside to be uniform. We can apply Ampere's Law to the
loop
(1)
If there are
turns
of wire per metre of the solenoid them the loop
will
enclose
turns
of wire, each carrying a current I, so will enclose a total current
of
The
right hand side of (1) is then
As for the left hand side, outside the coil the magnetic field is
zero so this part of the path contributes nothing to the integral.
Inside the coil, the magnetic field is a uniform
so
for the coil of length
the
left hand integral is
Hence
cancels
from both sides to give