ĭB = B · A
ĭB = BA cos ș
ĭB = magnetic flux
B = magnetic field, A = area vector
ș = angle between field, area vector
Units: webers (Wb = T·m^2 )
What is the magnetic flux
through this surface?
ĭB = BAcosș
ĭB = (2.0 T)(3.0 m^2 )(cos 60°)
ĭB = 3.0 Wb
29.7 - Faraday’s law
Faraday discovered two ways to induce an emf. The first was by moving a wire through
a magnetic field; the second was by changing the strength of the magnetic field passing
through a stationary wire coil. In the latter case, the magnetic flux changed because flux
is proportional to the strength of the magnetic field.
In general, since flux is the product of the magnetic field strength, the surface area, and
the cosine of the angle between the field vector and the area vector, changing any of
these three factors changes the flux and induces an emf.
To consider changes in magnetic field strength, we use the apparatus shown to the
right. It is similar to Faraday’s equipment. Two wire coils are wrapped around a piece of
iron. Both coils are insulated so that no current can flow directly between them. The coil
on the left is connected to a variable current source, a device that can cause a current
that changes over time to flow through the coil. As the current in this coil changes, so
will the magnetic field that it creates.
The iron core facilitates the transmission of the magnetic field from within the left-hand
coil to within the coil on the right. We use two illustrations of the same configuration to
show what occurs. In Concept 1, you see the overall configuration: the variable current
source attached to a coil on the left, the changing magnetic field passing through the
iron core, and the current that is induced in the coil on the right. In Equation 1, we show
the view looking down the coil on the right. The increasing magnetic field points away
from you down the coil in this view, resulting in a counterclockwise induced current.
Let’s discuss in more detail what is happening in this system. The iron core ensures that the magnetic field passes essentially unchanged from
within one coil to the other. Since the field is perpendicular to the loops of the coil on the right, the magnetic flux passing through this coil
Changing magnetic flux and
induced emf
Change in magnetic field strength yields
change in magnetic flux
Flux change induces emf
emf drives induced current