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Faraday's Law of Electromagnetic Induction Calculator

Calculates the induced electromotive force (EMF) in a coil due to a changing magnetic flux.

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Induced EMF

Formula first

Overview

Faraday's Law of Electromagnetic Induction describes how a changing magnetic field through a coil of wire generates an electromotive force (EMF), which can drive an electric current. The law states that the magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage. The negative sign, often referred to as Lenz's Law, indicates that the direction of the induced EMF opposes the change in magnetic flux that produced it, a manifestation of energy conservation.

Symbols

Variables

N = Number of Turns, \Delta\Phi = Change in Magnetic Flux, \Delta t = Change in Time, \mathcal{E} = Induced EMF

Number of Turns
Change in Magnetic Flux
Change in Time
Induced EMF

Apply it well

When To Use

When to use: Apply this law when a conductor or coil is exposed to a time-varying magnetic field, or when a conductor moves through a magnetic field, to determine the resulting induced voltage. It is crucial for understanding generators, transformers, and other electromagnetic devices. Ensure consistent units for magnetic flux (Webers) and time (seconds).

Why it matters: Faraday's Law is fundamental to modern electrical engineering and technology, underpinning the operation of almost all electrical power generation. It explains how generators convert mechanical energy into electrical energy, how transformers efficiently change AC voltages, and is essential for designing induction motors, RFID systems, and many other devices that rely on electromagnetic induction.

Avoid these traps

Common Mistakes

  • Forgetting the negative sign or misinterpreting its meaning (Lenz's Law).
  • Confusing magnetic flux (Φ) with magnetic flux density (B).
  • Incorrectly using units, especially for time or magnetic flux.

One free problem

Practice Problem

A coil with 150 turns experiences a change in magnetic flux from 0.02 Wb to 0.08 Wb over a period of 0.5 seconds. Calculate the magnitude of the induced electromotive force (EMF) across the coil.

Number of Turns150 turns
Change in Magnetic Flux0.06 Wb
Change in Time0.5 s

Solve for:

Hint: Calculate the change in magnetic flux first.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Halliday, Resnick, Walker. Fundamentals of Physics.
  2. Griffiths, David J. Introduction to Electrodynamics.
  3. Wikipedia: Faraday's law of induction
  4. Halliday, Resnick, and Walker, Fundamentals of Physics
  5. Griffiths, David J. Introduction to Electrodynamics
  6. NIST Special Publication 330, The International System of Units (SI)
  7. Halliday, Resnick, Walker Fundamentals of Physics
  8. Griffiths Introduction to Electrodynamics