Physics
HS/Science
Unit: 10 Lesson: 01
Faraday’s Law Discussion Points
1. The induction rule is referred to as Faraday’s law of induction. The directional sense (Emf is not a
vector so “direction” is not used.) of the induced emf is referred to as Lenz’s law.
2. Ghost Magnet –
This is a semi-popular concept/term to help describe the sense of the induced current. The
induced emf produces a current in the coil, which has an associated magnet. This ghost magnet
is always induced in such a manner as to oppose the change in the inducing magnetic field (This
simplifies the clockwise counter clockwise discussion.) as viewed from which side of the coil
(complication and gives the directional sense of Lenz’s law), and this utilizes the right hand rule for
magnetic fields from a coil.
• Reviewing the images from the following site is useful: http://hyperphysics.phyastr.gsu.edu/hbase/hframe.html
•
Use the Phet Faraday’s law simulation which shows the magnetic field lines and the direction
of the ghost magnet. Remember, these simulations use electron current instead of
conventional current.
3. Terminology:
• The induced emf depends upon the change in a quantity called magnetic flux.
• B is called by several names, such as: magnetic field, magnetic flux lines, magnetic flux
density, and some others less common names.
• B has SI units of Tesla or Webbers per m2. The unit of magnetic flux is weber.
• A quantity called magnetic flux is defined in a technical manner, but summarized as the net
number of B lines passing through the area of the coil as the important quantity. If B is
perpendicular to the area (like a pencil pointing up from a table top), then the flux is simply B
multiplied by the area. If B and A are not perpendicular, then the angles must be taken into
account.
• We are commonly dealing with one or more “flat” area—coils. If the area is closed, like the
area of a sphere, then the number of flux lines will be zero, since each B line that passes in
through the area will also eventually pass out of the closed area. This is a result of the fact that
B fields loop back upon themselves.
4. Induced EMF = -N Δ(Flux) / Δt
This is Faraday’s law; the minus sign is often referred to as Lenz’s law. N is the number of turns in
the coil.
©2012, TESCCC
11/07/12
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Physics
HS/Science
Unit: 10 Lesson: 01
•
Flux is the (NET) number of magnetic field lines passing through the coil area.
•
The shape of the coil is not important; it is the area as expressed in m 2 that is desired.
Flux = BA
•
The emf is induced, even if the coil is not there. However, there will be no current flow
without wires etc. In other words, the emf is induced, whether the area with changing magnetic
flux has a coil or not.
•
The emf is not induced at a specific location, such as a battery, but rather it is induced
like an electric field around the loop, to push charged particles around the loop.
5. Some situations may be described in terms studied in the past or in terms of Faraday’s law. The
point to be made is that Faraday’s law is more general and does not contradict previous
knowledge.
An important example of this concept is the movement of a wire through a magnetic field.
Consider the diagram shown with the B field into the page. The value of the induced voltage is
EMF = BLv,
where B is the magnetic field strength, L is the length of the wire on the right side of the coil
“cutting” through the B field, and v is the velocity of the loop.
This equation can be derived by two ways. The first recognizes that the change in area per time
containing magnetic field Δ(A)/Δt = Lv, leading to the equation above.
A second way is to realize that the force on the charges in the wire F=qvB, leading to an induced
electric field E=vB, and since EL=EMF, the value of the EMF again becomes EMF=BLv.
6. There are several ways that the flux can change:
•
The size of the magnetic field can change – magnet approaches, electromagnet
changes.
•
The size of the area can change – like the coil above or some other possibilities.
•
The orientation of the area relative to the field can change – coil rotating in field.
•
The number of turns changing would be unusual, but would change the emf.
7. Basic equations related to Faraday’s law:
• Φ = BA: flux (Φ) = magnetic field (B) times the area (A) of the coil through which the field
passes.
o Webber = Tesla m2 (units)
•
Emf = N ΔΦ/Δt: induced voltage (emf) = change in flux per time through N coils
o Volts = Webber/ sec (units)
©2012, TESCCC
11/07/12
page 2 of 3
Physics
HS/Science
Unit: 10 Lesson: 01
•
Emf = Blv: induced voltage = length of wire l moving with speed v through magnetic field B
o Volts = (Tesla)(m)(m/sec) (units)
Example Problem:
• Find the emf induced in a coil, 10 cm on each side laying on a table, if the average magnetic
field into the table changes from 5 mT to 2 mT in 0.2 seconds. (The current would be
clockwise, as viewed from above; the emf would be 1.5 x 10 -4 volt.)
L = .1 m
B1 = 5 x 10-3 T
B2 = 2 x 10-3 T
Δt = 0.2 sec
©2012, TESCCC
emf = ΔΦ/Δt
(Area)(ΔB/Δt) = (.1)2 (3 x 10-3 )/.2 = 1.5 x 10-4 V
11/07/12
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