AcademyElectromagnetic Induction
Academy
Eddy Currents
Level 1 - Physics topic page in Electromagnetic Induction.
Principle
Eddy currents are circulating induced currents inside bulk conductors exposed to changing magnetic flux.
Notation
\(I_{\mathrm e}\)
eddy current in a conducting path
\(\mathrm{A}\)
\(R\)
effective resistance of the current path
\(\mathrm{\Omega}\)
\(\mathcal E\)
induced emf around the path
\(\mathrm{V}\)
\(P\)
thermal power dissipated
\(\mathrm{W}\)
\(\Phi_B\)
magnetic flux through a current path
\(\mathrm{Wb}\)
Method
Derivation 1: Closed paths inside a conductor
A solid conductor contains many possible closed conducting paths. Changing flux induces emf around those paths.
Induced emf
\[\mathcal E=-\frac{d\Phi_B}{dt}\]
Eddy current
\[I_{\mathrm e}=\frac{\mathcal E}{R}\]
Derivation 2: Heating
The induced currents dissipate energy in the conductor's resistance.
Joule heating
\[P=I_{\mathrm e}^2R\]
emf form
\[P=\frac{\mathcal E^2}{R}\]
Derivation 3: Magnetic braking
The eddy current's magnetic force opposes the motion that caused the flux change.
Lenz direction
\[\vec B_{\mathrm{eddy}}\text{ opposes the flux change}\]
Energy path
\[W_{\mathrm{mechanical}}\rightarrow \text{thermal energy}\]
Rules
These relations are model-level estimates for eddy current effects.
Eddy current
\[I_{\mathrm e}=\frac{\mathcal E}{R}\]
Heating
\[P=I_{\mathrm e}^2R\]
emf heating
\[P=\frac{\mathcal E^2}{R}\]
Examples
Question
Why does a falling magnet slow down in a conducting tube?
Answer
The moving magnet changes flux through loops in the tube wall. Eddy currents are induced, and their magnetic effects oppose the motion. Mechanical energy becomes thermal energy in the tube.
Checks
- Eddy currents need conducting material and changing flux.
- They can be useful for braking or harmful as heating losses.
- Slotted or laminated conductors suppress large current loops.
- The direction always follows Lenz's law.