What is the formula for Motional EMF?

The Motional EMF formula is e = B × L × v, where e—Motional EMF (V); B—Magnetic flux density (T); L—Length of the conductor (m); v—Velocity perpendicular to the field (m/s).

Motional EMF

Q: How do you calculate Motional EMF?

Use the formula e = B × L × v. When a conductor of length L moves with velocity v through a magnetic field B (perpendicular), a motional EMF is induced along it as the field pushes free charges to the ends. Enter the values you know in the calculator above and it solves for the remaining variable.

e = B · L · v

Calculator

Induced EMF

Flux Density

Conductor Length

Velocity

Result

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Formula

e = B × L × v

Description

When a conductor of length L moves with velocity v through a magnetic field B (perpendicular), a motional EMF is induced along it as the field pushes free charges to the ends. It is the special case of Faraday’s law for a moving conductor and is the basic generating action in every dynamo, alternator, and linear generator.

Variables

e — Motional EMF (V)
B — Magnetic flux density (T)
L — Length of the conductor (m)
v — Velocity perpendicular to the field (m/s)

Practical Notes

Only the component of velocity perpendicular to both the conductor and the field contributes. Reversing the motion or the field reverses the EMF polarity—the basis of AC generation as a loop rotates.

Related Concepts

All Fields & Electromagnetism formulas →

Coulomb’s Law Electric Field of a Point Charge Electric Potential of a Point Charge Gauss’s Law (Electric Flux) Lorentz Magnetic Force Force on a Current-Carrying Wire Force Between Parallel Wires Magnetic Field of a Straight Wire

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