How to Calculate EMF From Magnetic Flux

The electromotive force is actually not a force at all, but work divided by charge. A battery, generator, solar cell or even cells in your body can provide that work. Often, EMF is associated with a battery in a circuit, but when a generator produces an EMF, it does so through a magnetic field. The magnetic flux is the magnetic field through a surface area, and if it is known (or able to be calculated), then the EMF due to that magnetic flux can be calculated. While the process is simple, it requires knowledge of calculus, specifically, how to integrate, take a derivative and calculate a dot product.

Things You'll Need

  • Mathematical computing program (optional)
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Instructions

  1. Determine Magnetic Flux

    • 1

      If the magnetic field is not uniform across a surface (its magnitude and direction change depending on where it crosses the surface), take the dot product of the magnetic field with the vector whose magnitude is the infinitesimal (or differential) area through which the magnetic field passes and whose direction is normal to the surface area and points outward.

    • 2

      Integrate the dot product found in Step 1 to find the magnetic flux as a function of time.

    • 3

      If the magnetic field is uniform, instead take the dot product of the field with the vector whose magnitude is the entire area, and whose direction is normal to the surface area and points outward.

      Note that the magnetic field may (and probably will) change over time, even if it is uniform with respect to position.

    Calculate EMF

    • 4

      Take the derivative of the flux, calculated in Section 1, with respect to time.

    • 5

      Multiply the answer in the previous Step by -1 to find the EMF. Note that, while the magnetic field is a vector, both the magnetic flux and the EMF are scalar quantities.

    • 6

      Label your answer with the proper unit. The Standard International unit of EMF is Volts (V).

    • 7

      To calculate the EMF in a coil, multiply the answer in Step 2 by the number of times the coil is wound in a circle.

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