Generally, we use the dot convention to represent the direction in which an inductor (or coil) is wound and inherently (when there is a change in flux linkage) to find the direction of the induced current . Direction of induced e.m.f is deduced using the Lenz's law.
However, in a text book I found the term 'negative mutual inductance', to justify the voltage induced in the opposite direction due to mutual inductance.
Could anyone comment on, how far it is acceptable to use this nomenclature in scientific writing.
This is just a matter of defining in which your winding turns are directed. Two opposite turned coils give a negative Lm, but again that is just a matter of connecting the coils. I would suggest to change the direction in the schematic, so you can use a positive Lm in any case.
Also take care of the turns ration, this is also influencing the value of the Lm in a not understandable way, better to use the T equivalent schematic and a separate ideal turns-ratio transformer(without inductance)
Mutual inductance is generically defined as M = |M|*Cos(theta). Thus if the two coils are placed at 90 degrees to one another the mutual inductance is zero and is a maximum (+1) when they are co-linear or at 0 degrees and minimum (-1) at 180 degrees.
Mathematically this equates to a dot product.
Thus mutual inductance can be positive Cos(0) = 1 or negative Cos(180) = -1 which is equivalent to the coils being wound in the same direction or opposite direction respectively.
However, take care as two coils physically placed at 90 degrees to one another in air are not the same as two coils placed physically 90 degrees to one another on a magnetic core as the latter is still 0 or 180 degrees.
@Gregory Diana: According to your definition of mutual inductance as a function of the angle between the coils, it seems like the mutual inductance is a vector quantity.
Could you please give me the reference that presents this definition.
(I just want to make sure that it is ok to use such terminology as 'negative mutual inductance' in scientific writing.)
Have a look in any electrical machines theory book.
Most electrical network theory book show M=k*sqrt(L1*L2) and omit the Cos(theta) as they assume the coils are on the same magnetic core or limb. k = coupling coefficient.
Hence my comment in this regard.
or k =M^2/(L11*L22)=M^2/( (L1+M)*(L2+M) ).
This says coupling coefficient is 1 if there is no leakage (ie L1=L2=0 (so all flux is mutual)
I will see if I can find and scan in and send.
It is well known that flux is defined as theta = B.A or BACos(theta)
see
http://www.physics.fsu.edu/courses/Spring13/PHY2054C/lect7-ch22__3notes.pdf
slides 3,4 & 5
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