PROFESSOR: For a many turn coil the surface
used to define the flux linkage is often geometrically complex.
For this three turn coil the surface
is filled in by stringing yarn between a vertical rod joining
the terminals in the external region to points on the wire.
The surface is filled in by connecting points on the rod
to points of increasing distance along the wire.
We have wound the few inductors of different lengths
a number of turns on a wooden rod,
using copper wire covered with enamel insulation.
The enamel insulation prevents electrical contact
between turns so the current path must follow the wire.
The insulation prevents short circuiting between turns.
We will measure the coil inductance using this meter.
We have twisted the terminal lens of this coil
to reduce the stray inductance.
It is wound on the non magnetic rod which
has a radius of 5 millimeters.
This coil has 50 turns and is 5.05 centimeters long.
The coil inductance is predicted to be 4.9 microhenrys.
The inductance meter measures the coil inductance
at 1 kilohertz.
This frequency is high enough that the coil inductive
reactants greatly exceeds the small coil of resistance,
which we have neglected in our analysis.
We measure 5.9 microhenrys.
This inductance has contributions from the coil
and connecting wires.
We short circuit the terminals and measure 0.7 microhenrys
as the lead inductance, subtracting
this from the measured 5.9 microhenrys
gives the coil inductance is 5.2 microhenrys.
A reasonable agreement with the predicted 4.9 microhenrys.
We now measure the inductance of the coil
with double the number of turns, but also double the length.
Doubling the number of turns N but also
doubling the coil length D should result
in double the inductance.
The inductance meter now reads 11.2 microhenrys subtracting
the 0.7 microhenrys lead inductance
gives corrected coil inductance of 10.5 microhenrys,
about double the inductance of the first coil of 5.2
microhenrys, as it should be.
We now measure the inductance of the coil which
is the same length as the second coil,
but has two layers of windings and thus double
the number of turns.
We measure 44.4 microhenrys for which the corrected coil
inductance is 43.7 microhenrys.
We have doubled the number of turns
without changing the coil length.
The coil area of the two layer coil
has hardly changed because the wire diameter
is much smaller than the wood diameter used as a core form.
The induction should increase by 4.
This coil inductance is about 4 times our previous corrected
measurement of 10.5 microhenrys with half the number of turns.
The surface for many turn coil used in Faraday's law
is geometrically complex as the bounding contour to the surface
follows the path of the wire.
For a tightly wound coil the magnetic flux
linking this surface is the sum of fluxes linking each turn.
Since the magnetic flux per turn is
proportional to the number of turns,
if each turn links the same flux,
the total flux linked by the coil
is N times the flux per turn.
The coil self-inductance is then proportional to the square
of the number of turns.