# Faraday's Law Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Dec 28, 2023

This Faraday's law calculator will help you find the electromotive force induced in a closed circuit. In this accompanying article, we will:

• Find out what electromagnetic induction is;
• See the difference between magnetic field and flux; and
• Cover Lenz's law and Faraday's law formula.

## 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 we place stationary electrons in a varying magnetic field, they induce an electromotive force (EMF), and a 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 $\Phi$ – 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 switch between them easily. A represents the cross-sectional area of the coil in which the EMF is induced.

$\small \Phi = \Beta \cdot \Alpha$

The following formula links teslas and webers:

$\small 1\ \text{Wb} / 1\ \text m^2 = 1\ \text T$

## 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:

$\small \varepsilon = \frac{d\Phi}{dt}$

where:

• $\varepsilon$ – Electromotive force (EMF);
• $d\Phi$ – Small change in magnetic flux; and
• $dt$ – Small change in time.

Lenz's law is the fundamental second law that describes electromagnetic induction. It doesn't define 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 Faraday's law with a minus sign:

$\small \varepsilon = -\frac{d\Phi}{dt}$

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 $N$:

$\small \varepsilon = -N\frac{d\Phi}{dt}$

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

Faraday had been an extremely productive scientist and developed a keen interest in everything related to electricity: not only in physics but also in chemistry. You can learn more about a different Faraday's law at our Faraday's law of electrolysis calculator.

🙋 Not sure how to find the rate of change? Worry not! Check our average rate of change 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 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 the magnetic field and the cross-sectional area:

\small \qquad \begin{align*} d\Phi &= \Beta \cdot \Alpha\\ &= 0.4 \times 30 \times 10^{-4}\\ &= 0.0012\ \text{Wb} \end{align*}
1. Now, determine how long it takes the magnetic field to change by 0.4 T. We can assume it took 8 seconds.

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

\small \qquad \begin{align*} \varepsilon &= -N\frac{d\Phi}{dt}\\[.5em] &= -10 \times 0.0012 / 8\\ &= -0.0015\ \text V \end{align*}

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

## Similar calculators

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

Bogna Szyk
Area of the loop
in²
Number of turns of the loop
turns
Magnetic field
T
Magnetic flux
Wb
Time
sec
Induced voltage
V
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