Faraday's Law of Electromagnetic Induction
Describes how a changing magnetic field induces an electric field (and thus an electromotive force).
What is Faraday's Law of Electromagnetic Induction?
The production of an electromotive force (voltage) across an electrical conductor in a circuit due to the conductor's movement through a magnetic field or a changing magnetic field.
Key formula / rule: Faraday's Law of Induction
Key points
- To understand the relationship between changing magnetic flux and induced EMF.
- To be able to calculate the induced EMF using Faraday's Law.
- To apply Lenz's Law to determine the direction of induced current.
- To recognize the applications of electromagnetic induction in real-world devices.
Common exam trap
Forgetting the negative sign in the formula, which relates to Lenz's Law.
Definitions
- Term
Electromagnetic Induction
- Meaning
The production of an electromotive force (voltage) across an electrical conductor in a circuit due to the conductor's movement through a magnetic field or a changing magnetic field.
- Term
Magnetic Flux (ΦB)
- Meaning
A measure of the total magnetic field passing through a given area. It is the surface integral of the magnetic field strength over that area.
- Term
Electromotive Force (EMF, ε)
- Meaning
The energy per unit charge given to the charge carriers when charge is transferred from a lower to a higher potential. It is the voltage developed by any source of electrical energy.
- Term
Lenz's Law
- Meaning
The direction of induced current in a conductor, due to a change in magnetic flux, is such that it opposes the change in magnetic flux that produced it.
Learning objectives
To understand the relationship between changing magnetic flux and induced EMF.
To be able to calculate the induced EMF using Faraday's Law.
To apply Lenz's Law to determine the direction of induced current.
To recognize the applications of electromagnetic induction in real-world devices.
Formulae
- Name
Faraday's Law of Induction
- Note
\ε is the induced electromotive force (EMF), and \ΦB is the magnetic flux.
- Expression
\ε = -\frac{d\ΦB}{dt}
- Name
Magnetic Flux (Uniform Field)
- Note
B is the magnetic field strength, A is the area, and \θ is the angle between B and the normal to the area.
- Expression
\ΦB = B \· A \cos\θ
- Name
Magnetic Flux (Non-uniform Field)
- Note
Integral over the surface area.
- Expression
\ΦB = \int B \· dA
Prerequisites
Understanding of magnetic fields and magnetic field lines.
Concept of magnetic flux.
Basic calculus (differentiation).
Understanding of electric current and electromotive force (EMF).
Common mistakes
Forgetting the negative sign in the formula, which relates to Lenz's Law.
Confusing magnetic flux with magnetic field strength.
Assuming EMF is induced even when the magnetic flux is constant.
Incorrectly calculating the change in magnetic flux when area or angle changes.
Keywords
Electromagnetic Induction
Faraday's Law
Magnetic Flux
Induced EMF
Lenz's Law
Rate of Change
Generator
Transformer
Practice preview
According to Faraday's law of electromagnetic induction, an electromotive force (EMF) is induced in a circuit whenever there is a change in:…
easy
A conducting rod of length L moves with a velocity v perpendicular to a magnetic field B. What is the magnitude of the induced EMF across the ends of the rod?…
easy
A coil with 500 turns has a magnetic flux of 2 x 10⁻³ Wb passing through it. If the flux is reversed in 0.1 seconds, what is the average induced EMF?…
medium