What is magnetic flux?
What is magnetic flux?
If the blue surfaces shown in Figure 1 both have equal area and the angle is , how much smaller is the flux through the area in Figure 1-left vs Figure 1-right?
How do we measure magnetic flux?
Figure 2 shows a map of a non-uniform magnetic field measured near a sheet of magnetic material. If the green line represents a loop of wire, what is the magnetic flux through the loop?
Figure 2: A map of magnetic field measurements around a loop of wire (green)
Why is this useful?
- When a coil of wire is moved through a magnetic field a voltage is generated which depends on the magnetic flux through the area of the coil. This is described by Faraday's law and is explored in our article on Faraday's law. Electric motors and generators apply Faraday's law to coils which rotate in a magnetic field as depicted in Figure 3. In this example the flux changes as the coil rotates. The description of magnetic flux allows engineers to easily calculate the voltage generated by an electric generator even when the magnetic field is complicated.
Figure 3: Simplified diagram of a rotating coil in an electric generator (public domain).
- Although we have thus-far only concerned ourselves with magnetic flux measured for a simple flat test-area, we can make our test-area a surface of any shape we like. In-fact, we can use a closed surface such as a sphere which encloses a region of interest. Closed surfaces are particularly interesting to physicists because of Gauss's law for magnetism. Because magnets always have two poles there is no possibility (as far as we know) that there is a magnetic monopole inside a closed surface. This means that the net magnetic flux through such a closed surface is always zero and therefore all the magnetic field lines going into the closed surface are exactly balanced by field lines coming out. This fact is useful for simplifying magnetic field problems.
Magnetic flux around a current-carrying wire
Figure 4 shows a square loop of wire placed near a current carrying wire. Using the dimensions shown in the figure, find the magnetic flux through a coil. If you don't know how to calculate the magnetic field around a wire, review our article on the magnetic field. Hint: it may be useful to plot the magnetic field vs vertical distance from the wire.
Figure 4: Magnetic flux through a loop near a straight current carrying wire.