Motional EMF

e = B · L · v

Quick answer

This calculator solves e = B × L × v for Induced EMF. With Flux Density 0.5 T, Conductor Length 10 cm, Velocity 10 m/s, the result is 0.5 V. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Induced EMF (V)
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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.

Symbols and units

Symbol Meaning Default unit Accepted units
e Induced EMF V pV, nV, µV, mV, V, kV
B Flux Density T G, mT, T
L Conductor Length cm mm, cm, m, km
vel Velocity m/s mm/s, m/s, km/s

Step by step

  1. 1. What you know: Flux Density 0.5 T, Conductor Length 10 cm, Velocity 10 m/s
  2. 2. The relation: e = B × L × v
  3. 3. Substitute: B = 0.5 T, L = 10 cm, vel = 10 m/s
  4. 4. Result: Induced EMF = 0.5 V

Worked examples

Minimum range

Given: Flux Density 10 G, Conductor Length 1 mm, Velocity 10 mm/s

Result: Induced EMF = 10 nV

Low range

Given: Flux Density 10 mT, Conductor Length 10 mm, Velocity 100 mm/s

Result: Induced EMF = 10 µV

Typical

Given: Flux Density 0.5 T, Conductor Length 10 cm, Velocity 10 m/s

Result: Induced EMF = 0.5 V

High range

Given: Flux Density 1.5 T, Conductor Length 1 m, Velocity 100 m/s

Result: Induced EMF = 150 V

Maximum range

Given: Flux Density 15 T, Conductor Length 10 m, Velocity 1 km/s

Result: Induced EMF = 150 kV

Solving for each variable

Solve for Induced EMF

Flux Density 10 G, Conductor Length 1 mm, Velocity 10 mm/s → 10 nV

Solve for Flux Density

Induced EMF 0.33 V, Conductor Length 1 mm, Velocity 10 mm/s → 33000 T

Solve for Conductor Length

Induced EMF 0.33 V, Flux Density 10 G, Velocity 10 mm/s → 33 km

Solve for Velocity

Induced EMF 0.33 V, Flux Density 10 G, Conductor Length 1 mm → 330 km/s

How Induced EMF changes with Flux Density

Flux Density (input) Induced EMF (result)
50 mT 50 mV
125 mT 125 mV
0.25 T 0.25 V
0.375 T 0.375 V
0.5 T 0.5 V
0.75 T 0.75 V
1 T 1 V
2 T 2 V
3.5 T 3.5 V
5 T 5 V

The same result in other units

Unit Value
µV 500000
mV 500
V 0.5
kV 0.0005

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Frequently asked questions

How do you calculate Motional EMF?

Use e = B × L × v. With Flux Density 0.5 T, Conductor Length 10 cm, Velocity 10 m/s, Induced EMF works out to 0.5 V.

What is the formula for Motional EMF?

The formula is 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.

How do you find Flux Density when you know the other values?

Rearrange for Flux Density: with Induced EMF 0.33 V, Conductor Length 1 mm, Velocity 10 mm/s, Flux Density is 33000 T.

How do you find Conductor Length when you know the other values?

Rearrange for Conductor Length: with Induced EMF 0.33 V, Flux Density 10 G, Velocity 10 mm/s, Conductor Length is 33 km.

What units does Motional EMF use?

Induced EMF is shown in µV, mV, V, kV. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

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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