The Faraday's Law simulation models how a changing magnetic flux creates an electromotive force (an emf), -dΦ/dt = emf. The magnetic flux Φ is a measure of the amount of magnetic field flowing perpendicularly through an area and the emf is the voltage that is observed along the area's perimeter. The flux Φ is given by B • A for a uniform magnetic field and constant area. For non-uniform fields, we perform an average using a surface integral:
In this simulation, the magnetic field is perpendicular to the computer screen and the magnitude is given by the function B(x,t). This field strength is shown using color to indicate the field's direction and magnitude. Blue indicates the magnetic field is into the page; red indicates it is out of the page. The intensity of the color is proportional to the magnitude of the magnetic field. Position is given in meters, magnetic field strength is given in milliTesla, emf is given in millivolts, and the animation time is given in seconds. Note that the animation time is faster than real time..
Consider a constant magnetic field. Set B(x,t) = 1 to produce a uniform magnetic field with constant magnitude. The Φ output shows the flux passing through the area enclosed by the wires. The separation between the two horizontal wires is 6 m. Slide the wire and notice that the emf remains zero because the simulation clock is not running. Press the Play button to start the clock and drag the wire. Note that an emf is produced as you drag the wire. The direction of current in the loop is indicated by the current arrow below the loop.
Consider a changing magnetic field. Set B(x,t) = sin(pi*t/10) to produce a uniform magnetic field that varies sinusoidally. The graph shows the induced emf in the wires as a function of time. The direction of current in the loop is indicated by the current arrow below the loop.
Notice that, for the first 10 s of the animation, there is a decreasing flux through the loop as the magnetic field changes from out to into the screen. Also notice that there is an emf induced in the wire loop and an induced current. Is the induced current in the loop in the direction you would expect from Faraday's Law? The induced current may be in the opposite direction as you expected. Because of the minus sign in Faraday's law (Lenz's law), the emf is the negative of the slope of the flux vs. time graph. From t = 0 s to t = 5 s the magnetic field is increasing and therefore the emf is negative. Now watch the animation for the remaining time and see how the emf changes with time. How does the emf graph change if the slider is moved to the left? Right?
Consider a non-uniform field. Set B(x,t) = sin(pi*x/2) to produce a constant non-uniform magnetic field. Drag the wire from the left to the right side of the circuit and note the emf in the top window. Compare the shape of the emf graph from the first animation with the that from the second animation. What do you notice? Since the emf is related to the changing flux, it does not matter if that changing flux is due to a changing magnetic field or a changing area. In fact, a changing magnetic flux can be due to a changing magnetic field, a changing area, or both.