Created by Krishna Nelaturu
Last updated: Sep 14, 2022

Our Faraday's law calculator will help you determine the amount of voltage induced in a coil by a changing magnetic field. If you had trouble understanding electromagnetic induction, Faraday's law, and Lenz's law, you've come to the right place! Here, we shall go through the fundamentals of electromagnetic induction, including:

• Faraday's law, Lenz's law, and electromagnetic induction.
• Magnetic flux formula.
• Formula for induced voltage or EMF (electromotive force).

If you're interested in electric potential instead, head to our electric potential calculator.

## What is electromagnetic induction?

Take a coil of insulated copper wire and connect it to a galvanometer to form a circuit. The galvanometer points to zero because there is no voltage source like a battery in the circuit to drive an electric current.

Now place a magnet close to this coil. When the magnet is stationary, the galvanometer once again indicates no current. But when we move the magnet towards the coil, the galvanometer shows that some current is passing through the circuit. Moving the magnet away from the coil shows a similar galvanometer deflection in the opposite direction. But what is driving this current if there is no battery or cell in the circuit?

Electromagnetic induction is the phenomenon that induces an electromotive force (or voltage) in a circuit in the presence of changing magnetic field.

Micheal Faraday described this phenomenon in his law in 1831. But first, let's learn about magnetic flux.

## A formula for magnetic flux

Magnetic flux through a surface is a measure of the magnetic field passing through that surface perpendicularly. Some interpret it as the number of magnetic field lines passing through this surface.

The formula for magnetic flux is:

$\Phi = B \cdot A$

Where:

• $\Phi$ - Magnetic flux, measured in Webers $\text{Wb}$;
• $B$ - Magnitude of the magnetic field, measured in teslas $\text{T}$; and
• $A$ - Cross-sectional area of the coil in $\text{m}^2$.

Before calculating electromagnetic induction, we first use this equation to calculate the flux through the coil.

## Faraday's law and Lenz's law| Induced voltage formula

Faraday's law states that the induced electromotive force (or voltage) in a coil is directly proportional to the time rate of change of the magnetic flux:

$\varepsilon \propto \frac{\text{d}\Phi}{\text{d}t}$

Where:

• $\varepsilon$ - Induced electromagnetic force (emf);
• $\text{d}\Phi$ - Small change in the magnetic flux; and
• $\text{d}t$ - Time it takes for the change in the magnetic flux.

Lenz's law states that the direction of this induced emf is such that the magnetic field generated by this induced current opposes the change in the external magnetic flux. Combining this with Faraday's law, we get a formula for the emf induced:

$\varepsilon = - \frac{\text{d}\Phi}{\text{d}t}$

If there are $N$ windings or turns in the coil, the induced emf formula must account for this:

$\varepsilon = -N \frac{\text{d}\Phi}{\text{d}t}$

This Faraday's law formula for induced voltage applies to all electromagnetic induction calculations.

## How to use this Faraday's law calculator?

Armed with our Faraday's law calculator, you can perform electromagnetic induction calculations within a heartbeat:

• Provide the number of turns in the coil.
• Enter the area of the conductor loop and the magnitude of the magnetic field. This tool will automatically calculate the flux through the coil.
• Give the time in which the magnetic flux changes.
• Our Faraday's law calculator will instantly tell you the induced voltage in the circuit.

Want to understand the relation between voltage and current in a loop? Visit our Ohm's law calculator.

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