Motional EMF Calculator
Enter magnetic field, conductor length, velocity and resistance to compute motional EMF and induced current.
Input Data
Results
At a glance:Motional EMF arises when a conductor moves through a magnetic field. A charge q in the conductor experiences magnetic force qv×B, which separates charges and creates a potential difference across the ends. For a straight rod of length L moving perpendicular to B at speed v, the EMF is ε = B·L·v. If the rod is part of a closed circuit of resistance R, the induced current is I = ε/R (Lenz's law gives its direction, opposing the change in flux). This is the principle behind generators and rail guns.
Formula
Motional EMF: ε = B·L·v
Induced current: I = ε/R
$$\varepsilon = BLv, \quad I = \frac{\varepsilon}{R}, \quad F = BIL = \frac{B^2 L^2 v}{R}, \quad P = \frac{\varepsilon^2}{R} = \frac{B^2 L^2 v^2}{R}$$How to Use
- Enter the magnetic field B (T).
- Enter the conductor length L (m).
- Enter the velocity v (m/s).
- Enter the resistance R (Ω).
- The calculator returns EMF and current.
Case Studies
Rod in a field
B = 0.5 T, L = 0.3 m, v = 2 m/s, R = 1 Ω.
ε = 0.5×0.3×2 = 0.3 V.
I = 0.3/1 = 0.3 A.
FAQ
Why is the direction given by Lenz's law?
Lenz's law states the induced current opposes the change in magnetic flux that produced it, conserving energy. The magnetic force then does negative work on the external agent moving the rod.
What if motion is not perpendicular to B?
Only the component of v perpendicular to B contributes: ε = B·L·v·sinθ where θ is the angle between v and B.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.