I'm really having a problem understanding magnetic flux
and Lenz's Law of electromagnetic induction. I'm beginning to feel really
stupid and the explanations I read are confusing me more and more. Can
you help????? I'd be really grateful.
Sometimes exactly the same words with an entirely different mental
picture helps me get something I've been having trouble with: think of
wind going through a hula hoop. Wind velocity is going to play the
role of the magnetic induction B, and the hula hoop is going to
represent a wire loop. Wind velocity is a vector field: it varies both
in magnitude (breezy here, calm over there) and in direction (it can
come from the north or from the south, and it can swirl around). A
magnetic field can't be more complicated than the wind because they're
both just vector fields.
The magnetic flux through a wire loop is exactly analogous to the
amount of air going through the hula hoop. It's the dot product of the
field strength and the cross-sectional area of the loop. Turn the hula
hoop edge-on to the wind and the flux drops to zero because no air is
getting through it. Keep turning and the flux goes negative because
now the wind is blowing the other way through the hoop.
Now Faraday's law says the force on charges in the wire loop depends
on the *change* in flux through the loop. The charges don't care how
strong the wind is; they only care how rapidly the amount of air going
through the hoop changes. If you rotate the hoop very quickly in a
light breeze, they'll get excited. If it's really windy, a very slow
rotation will do the same thing. If it's gusty, you can leave the
hoop stationary and the change in wind speed will do the trick.
These days, most hula hoops have beads in them. Let's pretend that if
the beads move inside the hoop they will generate wind through the hoop.
Let's say if they go clockwise, they generate a wind going in the direction
a screw would go if the beads were turning it. Let's say if you increase
the amount of air going in that same direction through the hoop, the beads
will feel forced to move (so far we have Faraday's law) counter-clockwise
(now we've added Lenz's law).
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Update: June 2012