University of Wisconsin Green Bay

You want to design a generator that produces a peak EMF of 120 V and goes through 60 complete cycles every second. If you are able to produce a magnetic field of 0.15 T, how many coils of wire do you need on the armature? The cross sectional area of one of your loops is 0.71 m2.

  • In this problem, you are asked to relate the EMF produced in a rotating loop of wire to the construction of that loop. Whenever you induce EMF or current in a loop by changing the magnetic flux through the loop, the physics you need to consider is induction.

    So this is an induction problem. EMF in this loop is due to the changing magnetic flux through the loop as it rotates in the magnetic field.

  • In this problem, you are not asked for direction of current and so will not need to use the right hand rule. For that reason, a picture is not really needed. However, it may help you to visualize the problem. The key to induction in a generator is that a coil of wire rotates in the presence of a magnetic field.

  • Magnetic induction problems always begin with the definition of EMF:

    EMF = -N ΔΦ/Δt = -N Δ(BA cosθ)/Δt (Calculus students use d rather than Δ.)

  • No further mathematical solution is needed.

  • In this problem, you are asked to design a generator that will have a peak induced EMF of 120 V. In general, if there is no source of voltage difference in a circuit, you should consider induction as the cause of current even though the word induction was not used in the problem. In this case, the magnetic flux through the loop continually changes because the loop. A changing magnetic flux results in an EMF, which has the same effect in a circuit as a voltage difference.