Faraday's Law | Engineering Calculator API

Use the Faraday's Law calculator to solve electromagnetic induction problems by computing the induced EMF, change in magnetic flux, time interval, or number of coil turns. This endpoint implements Faraday's Law of Induction:

$\epsilon = -N\frac{\Delta \Phi}{\Delta t}$

I also included support in calculating magnetic flux from a changing magnetic field:

$\Phi = B \cdot A \cdot cos(\theta)$

This makes it useful for physics students, electrical engineers, and circuit designers working with generators, inductors, transformers, and magnetic fields.

What This Function Solves

The Faraday's Law solver can compute any missing variable:

• Induced EMF (voltage, $\epsilon$)

• Change in magnetic flux ($\Delta \Phi$)

• Time interval ($\Delta t$)

• Number of turns ($N$)

It also supports:

• Flux derived from magnetic field ($B$) and area

• Initial and final values for flux, magnetic field, and time

• Optional angle $\theta$ between field and surface

• Signed or unsigned EMF results

Input Parameters

For the standard Faraday's Law equation:

If you need to compute magnetic flux, use the magnetic field mode:

Additional Parameter

How the Solver Works

The API determines the missing variable automatically based on the inputs you provide.

Solve for EMF

$\epsilon = -N\frac{\Delta \Phi}{\Delta t}$

Requires:

• N

• flux (or flux_i and flux_f)

• t (or t_i and t_f)

For all the following, assume that t and flux can be interchanged with t_i, t_f and flux_i, flux_f, respectively.

Solve for Change in Flux

$\Delta \Phi = \frac{\epsilon \cdot \Delta t}{N}$

Requires:

• emf

• N

• t

Solve for Time Interval

$\Delta t = \frac{N \cdot \Delta \Phi}{\epsilon}$

Requires:

• emf

• N

• flux

Solve for Number of Turns

$N = \frac{\epsilon \cdot \Delta t}{\Delta \Phi}$

Requires:

• emf

• t

• flux

Example Use Cases

1. Calculate Induced Voltage in a Coil

Find EMF when magnetic flux changes through a coil:

1{
2  "law": "faraday",
3  "vars": {
4    "N": 200,
5    "flux_i": 0.01,
6    "flux_f": 0.05,
7    "t": 0.2
8  }
9}

2. Use Magnetic Field Instead of Flux

1{
2  "law": "faraday",
3  "vars": {
4    "N": 500,
5    "B_i": 0.2,
6    "B_f": 0.8,
7    "area": 0.01,
8    "theta": 0,
9    "t": 0.05
10  }
11}

3. Solve for Number of Turns Needed

1{
2  "law": "faraday",
3  "vars": {
4    "emf": 12,
5    "flux": 0.002,
6    "t": 0.01
7  }
8}

Returned Output

The response includes: