http://www.ck12.org Chapter 14. Magnetism
In the example to the left, there are four loops of wire(N= 4 )and each has areaπr^2. The magnetic field is pointing
toward the top of the page, at a right angle to the loops. Think of the magnetic flux as the “bundle” of magnetic field
lines “held” by the loop. Why does it matter? See the next equation
em f=−∆Φ
∆tThe direction of the induced current is determined as follows: the current will flow so as to generate a magnetic field
thatopposesthe change in flux. This is called Lenz’s Law.
If you change the amount of magnetic flux that is passing through a loop of wire, electrons in the wire will feel a
force (called the electromotive force), and this will generate a current. The equivalentvoltage(emf) that they feel
is equal to the change in flux 4 Φdivided by the amount of time 4 tit takes to change the flux by that amount.
This is Faraday’s Law of Induction. The relative direction of the loops and the field matter; this relationship is
preserved by creating an ’area vector’: a vector whose magnitude is equal to the area of the loop and whose direction
is perpendicular to the plane of the loop. The directions’ influence can then be conveniently captured through a dot
product:
Φ=N~B·~A Electromagnetic FluxThe units of magnetic flux are T×m^2 , also known asWebers(Wb).
In the example above, there are four loops of wire(N= 4 )and each has areaπr^2 (horizontally hashed). The magnetic
field is pointing at an angleθto the area vector. If the magnetic field has magnitudeB, the flux through the loops
will equal 4 cosθBπr^2. Think of the magnetic flux as the part of the “bundle” of magnetic field lines “held” by the
loop that points along the area vector.
If the magnetic flux through a loop or loops changes, electrons in the wire will feel a force, and this will generate a
current. Theinduced voltage(also calledelectromotive force, or emf) that they feel is equal to the change in flux
4 Φdivided by the amount of time 4 tthat change took. This relationship is called Faraday’s Law of Induction:
em f=−∆Φ
∆tFaraday’s Law of Induction