I will be introducing Lenz's "law" this week. Before
formulating it in the most general (verbal) form I plan
to focus on the negative sign in the Faraday's Law
using a simple illustration. Two concentric circles
will be drawn. The slightly larger circle will represent
the primary loop; its current, I1, will be clockwise.
The smaller circle will represent the secondary loop,
in the same plane.
Faraday discovered that the induced current, I2, is
clockwise when I1 is decreasing and that it is
counterclockwise when I1 is increasing. The current
I2 is said to be a consequence of the induced emf
(whose direction is the same as that of I2).
Mathematically the induced emf is described as:
emf = - d(FLUX)/d(TIME)
The negative sign is necessary because the current I2
increases (from zero) when dI1 is negative and
decreases when dI1 is positive. These are well
established experimental facts. Changes in I1 and the
resulting changes in I2 are linked like action and
reaction forces in mechanics. When one is positive
(for example, clockwise) the other is negative, and
vice versa. That is why there is the negative sign in
the above relation. I will also say that Faraday's Law
is a description of a cause-and-effect chain:
The magnetically induced emf is not localized, as in a loop
with a battery. The electric field, E, along our circular wire
loop, is equal to emf / (2*Pi*r). The direction of the induced
electric field is the same as the direction of conventional I2).
Other illustrations will add depth to Faraday's Law and to
Lenz's principle. The signs of delta(I1) and delta(I2) are
always opposite; this has nothing to do with which direction
(clockwise or couter-clockwise) is declared as positive in a
particular illustration.
Ludwik Kowalski