AcademyElectromagnetic Induction
Academy
Induction Observations
Level 1 - Physics topic page in Electromagnetic Induction.
Principle
Induction occurs when changing magnetic flux drives charge around a closed conducting path.
Notation
\(\Phi_B\)
magnetic flux through a surface
\(\mathrm{Wb}\)
\(\vec B\)
magnetic field
\(\mathrm{T}\)
\(A\)
surface area
\(\mathrm{m^{2}}\)
\(\theta\)
angle between \(\vec B\) and area normal
\(\mathrm{rad}\)
\(\mathcal E\)
induced emf around a loop
\(\mathrm{V}\)
\(I\)
induced current
\(\mathrm{A}\)
Method
Derivation 1: Define what changes
The useful scalar is magnetic flux: field component through a chosen surface, multiplied by area.
Flux definition
\[\Phi_B=\int\vec B\cdot d\vec A\]
Uniform field
\[\Phi_B=BA\cos\theta\]
Derivation 2: Identify induction
An induced emf is observed when the flux through a conducting loop changes. The change may come from changing field, area, orientation, or the circuit crossing field lines.
Flux change
\[\Delta\Phi_B\ne0\]
Induced emf
\[\mathcal E\ne0\quad\text{while flux changes}\]
Closed circuit
\[I=\frac{\mathcal E}{R}\]
Derivation 3: No change, no induction
A steady flux through a fixed loop gives no induced emf, even if the loop already sits in a magnetic field.
Steady flux
\[\frac{d\Phi_B}{dt}=0\]
No induced emf
\[\mathcal E=0\]
Rules
These observations prepare Faraday's law.
Magnetic flux
\[\Phi_B=\int\vec B\cdot d\vec A\]
Uniform flux
\[\Phi_B=BA\cos\theta\]
Closed circuit
\[I=\frac{\mathcal E}{R}\]
Examples
Question
A fixed loop sits in a steady uniform magnetic field. Is an emf induced?
Answer
No. The flux is nonzero, but it is not changing, so no induction is observed.
Checks
- Flux through a loop can change even if the loop area stays fixed.
- A magnetic field alone is not enough; the flux must change.
- The induced current exists only if the conducting path is closed.
- The sign and direction come from Lenz's law, not from flux magnitude alone.