This Faraday's law calculator will help you find the electromotive force induced in a closed circuit.

What is electromagnetic induction?

If you attached a metal wire to a battery, you would create a current - electrons would move along the wire. Then, if you put this wire in a magnetic field, an additional electric force would be induced by the motion of electrons in the field.

This effect also works in reverse - when stationary electrons are placed in a varying magnetic field, an electromotive force (EMF) is induced, and the current starts to flow. This phenomenon is known as electromagnetic induction.

Magnetic field and flux

The magnetic field has two main characteristics. The first one is the magnitude B of the field and is measured in teslas (symbol T), or newtons per meter per ampere. The second - magnetic flux Φ - is defined as the magnetic field passing through a surface, and is measured in webers (symbol Wb).

Magnitude and flux are interdependent - you can use the equation below to easily switch between them. A stands for the cross-sectional area of the coil, in which the EMF is induced.

Φ = B * A

Teslas and webers are linked by the following formula:

1 Wb / 1 m² = 1 T

Lenz's law and Faraday's law formula

Faraday's law states that the voltage induced in a circuit is equal to the rate of change - that is, change in time - of the magnetic flux through a loop:

EMF = dΦ / dt

Lenz's law is the key second law that describes electromagnetic induction. It doesn't describe the magnitude, but rather the direction of the current, stating that the current will always oppose the flux that produced it. It is incorporated into the Faraday's law with a minus sign:

EMF = - dΦ / dt

If you try to induce the electromotive force in a coil with multiple turns, you can also multiply this value by the number of turns to account for the number of turns N:

EMF = - N * dΦ / dt

This is the formula used by our Faraday's law calculator.

How to calculate the electromotive force?

Usually, you won't immediately know what is the magnetic flux in the coil. Don't worry, though - our electromagnetic induction calculator can find it, too! Just follow the steps below to calculate the induced voltage.

  1. Decide on the cross-sectional area and the number of turns in the loop. For example, you can use a circular coil with a cross-section of 30 cm² and with ten turns.

  2. Find out what is the magnitude of the magnetic field. For instance, we can assume a field of 0.4 teslas.

  3. Calculate the change in magnetic flux as the product of magnetic field and the cross-sectional area:

dΦ = B * A

dΦ = 0.4 * 30 * 10⁻⁴ = 0.0012 Wb

  1. Now, determine how long does it take the magnetic field to change by 0.4 T. We can assume that it took 8 seconds.

  2. Use the Faraday's law formula to calculate the electromotive force:

EMF = - N * dΦ / dt

EMF = - 10 * 0.0012 / 8 = -0.0015 V

The induced voltage is equal to 0.0015 V. The minus sign indicates that the direction of the current opposes the direction of the magnetic flux.

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If you liked this Faraday's law calculator, make sure to check out the Ohm's law calculator, too!

Bogna Haponiuk

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