Download Unit 08 Induction and Lenz`s Law

Electromagnetic Induction: Faraday’s Law and Lenz’s law
Physics 100L Exercise 8
Electromagnets
Last week we saw that moving electric charges (currents) could produce a
magnetic field, which we could “see” with a compass. The direction of this
magnetic field was given by the right-hand-rule that we discussed. In that
experiment we looked at the magnetic field produced by a straight wire, but
what would happen if we were to examine a loop of wire? The result would
An electromagnet
be what is known as an electromagnet, and it is pictured at right. If you
recall from last week, this is the same pattern that is produced by a
permanent bar magnet (in the figure the field lines will eventually loop around on the outside).
The direction of the magnetic field in this case is given by another right-hand-rule: curl your
fingers in the direction of the current and your thumb will point in the direction of the field. The
concept of electromagnets will come into play when we discuss Lenz’s Law. First, however, we
will look at the “reverse” law of the one we saw last week, which is that changing magnetic
fields produce moving charges.
Induction – Faraday’s Law
Michael Faraday discovered that by either moving a loop of wire through a magnetic field or by
changing the magnetic field through the loop, he could induce an electric current in the loop, an
effect that is now known as Faraday’s Law. This can be summarized in the following statement:
Faraday’s Law:
EMF 
Change in magnetic flux
elapsed time
where the EMF is the induced voltage that drives the current around the loop (EMF stands for
electromotive force, but that is a misnomer and is unimportant), the magnetic flux is the number
of B-field lines that cross through the enclosed area of the loop, and the elapsed time refers to the
time interval over which the change in flux takes place. Note that since we are inducing a
current in a loop of wire, the result will be an electromagnet. Thus, the changing magnetic flux
produces a current, which in turn produces another magnetic field. We will refer to the original
magnetic field (the one being changed) as the “external field” and the one produced by the
electromagnet as the “induced field.” Be sure that you understand the distinction and the fact
that there are two magnetic fields involved here.
Direction – Lenz’s Law
Lenz’s Law gives the direction of the currents induced by changing magnetic fluxes:
The direction of an induced current is such that it produces an electromagnet with an
orientation that opposes the influence that created it.
Recall that Faraday’s Law predicts an induced current only for a changing magnetic flux. What
Lenz’s Law states is that the electromagnet produced by the induced current will oppose the
change in magnetic flux – this is what Lenz means by the term “influence.” The induced
electromagnet does not oppose the original (external) magnetic field, but it opposes the change
in the external field. This is a very important distinction that confuses many people so I will
state it again: the induced electromagnet does not oppose the original (external) magnetic field,
but it opposes the change in the external field. Read that sentence again and again until you
understand it, and if you still can’t ask your TA to explain it until you do.
As a concrete example of these laws, consider a bar magnet that is dropped through a loop of
wire. The changing magnetic flux through the loop will induce a current in the loop, which will
turn the loop into an electromagnet. Since Lenz’s Law dictates that the electromagnet opposes
the change in flux, the direction of the magnetic field in the electromagnet will be such that it
tries to slow down the falling bar magnet.
This process can be illustrated in the following figures.
External field
(increasing)
Induced field
Induced current
Since we are trying to draw three-dimensional pictures in a two-dimensional space, we need to
establish conventions for what we mean by into the paper and out of the paper. In the above
figures these are represented as follows:
into the page
out of the page
The Experiment
We will demonstrate the effects of Faraday’s Law and Lenz’s Law using a coil of wire attached
to a galvanometer. The galvanometer measures current, so it will tell us if there is a current in
the wire – initially it should be stuck at zero since nothing is happening. Note that there is no
battery or other power source attached to the circuit, so any current that shows on the
galvanometer is coming from some other source, which in our case is induction. Follow the
directions on your worksheet and record what happens. Try to determine what is going on by
drawing appropriate sketches in the spaces provided – these sketches will look like the above
ones.