Faraday's Law Formula

The induced EMF in a circuit equals the negative rate of change of magnetic flux through the circuit.

The Formula

E=−NdΦBdt where N is number of turns and ΦB=BAcos⁡θ is magnetic flux.

When to use: The faster you change the magnetic field through a loop, the bigger the voltage you get. Faraday's law tells you exactly how much.

Quick Example

A coil with 100 turns in a field that drops from 0.5 T to 0 in 0.1 s: if the coil area is 0.01 m2, the induced EMF is 5 V.

Notation

E is the induced EMF in volts, N is the number of turns, ΦB is the magnetic flux in webers (Wb), B⃗ is the magnetic field in tesla, and dA⃗ is the differential area element.

What This Formula Means

The induced EMF in a circuit equals the negative rate of change of magnetic flux through the circuit.

The faster you change the magnetic field through a loop, the bigger the voltage you get. Faraday's law tells you exactly how much.

Formal View

Faraday's law states that the induced electromotive force in a closed loop equals the negative time derivative of magnetic flux: E=−NdΦBdt, where ΦB=∫B⃗⋅dA⃗.

Worked Examples

Example 1

medium
A coil with 100 turns experiences a change in magnetic flux from 0.05 Wb to 0.02 Wb in 0.1 s. What is the induced EMF?

Answer

E=30 V

First step

1
Faraday's law: E=−NΔΦΔt.

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Example 2

hard
A single loop of area 0.04 m2 is in a magnetic field that increases uniformly from 0 to 0.6 T in 0.3 s. What is the induced EMF?

Example 3

medium
A coil of 50 turns has a magnetic flux that changes from 0.02 Wb to 0.08 Wb in 0.1 s. Find the induced EMF.

Common Mistakes

  • Forgetting to multiply by the number of turns N — a coil with 100 turns produces 100 times more EMF than a single loop. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Ignoring the angle θ between the magnetic field and the area vector when computing flux (ΦB=BAcos⁡θ, not just BA). - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Dropping the negative sign and then getting the direction of induced current wrong — the sign encodes Lenz's law. - Fix this by naming the system, checking "Am I using a field or potential to explain how one object influences another across space?", and attaching units or direction to the final statement.
  • Using faraday's law from a keyword alone - Signal words like field, charge, magnet only point to a possible model; the system must match too.

Why This Formula Matters

Faraday's Law gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

Frequently Asked Questions

What is the Faraday's Law formula?

The induced EMF in a circuit equals the negative rate of change of magnetic flux through the circuit.

How do you use the Faraday's Law formula?

The faster you change the magnetic field through a loop, the bigger the voltage you get. Faraday's law tells you exactly how much.

What do the symbols mean in the Faraday's Law formula?

E is the induced EMF in volts, N is the number of turns, ΦB is the magnetic flux in webers (Wb), B⃗ is the magnetic field in tesla, and dA⃗ is the differential area element.

Why is the Faraday's Law formula important in Physics?

Faraday's Law gives students a way to explain non-contact forces and energy changes. It connects electricity, magnetism, gravitation, induction, motors, generators, and orbital motion through a shared spatial model.

What do students get wrong about Faraday's Law?

Students often know a formula related to faraday's law but skip the recognition step: Am I using a field or potential to explain how one object influences another across space? That leads to a correct-looking substitution attached to the wrong physical model.

What should I learn before the Faraday's Law formula?

Before studying the Faraday's Law formula, you should understand: electromagnetic induction.

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