http://www.ck12.org Chapter 15. Magnetism Version 2
By plugging equation [1] into equation [4], one can find the exact formula for this force (left to the reader — make
sure to remember that the two wires can have different currents).
Electromagnetic Induction
Changing magnetic fields passing through a loop of wire generate currents in that wire; this is how electric power
generators work. Likewise, a changing current in a wire will create a changing magnetic field; this is how speakers
and electric motors work.
To understand induction, we need to introduce the concept ofelectromagnetic flux. If you have a closed, looped
wire of areaA(measured in m^2 ) andNloops, and you pass a magnetic fieldBthrough, the magnetic fluxΦis given
by the formula below. Again, 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 [5] 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