Calculator Inputs
Formula Used
Motional electromotive force (emf) arises when a conductor moves through a magnetic field.
Charges experience the magnetic force q(v × B), producing a separation of charge and a potential difference.
For a straight conductor segment of effective length L moving at speed v in a field B,
the emf magnitude is:
ε = N · B · L · v · sin(θ)
- ε is motional emf (volts).
- B is magnetic flux density (tesla).
- L is effective conductor length cutting field lines (meters).
- v is speed of motion (m/s).
- θ is the angle between velocity and magnetic field.
- N scales emf for multiple turns or repeated segments.
How to Use This Calculator
- Enter the magnetic field strength B and choose its unit.
- Enter the effective conductor length L and choose its unit.
- Enter the speed v and select the velocity unit.
- Set the angle θ between v and B (default 90°).
- Optionally set N for multiple turns or repeated segments.
- Optionally enter resistance R to estimate current and power.
- Click Calculate. The result appears above the form.
- Use Download CSV or Download PDF for reports.
Example Data Table
| # | B (T) | L (m) | v (m/s) | θ (deg) | N | R (Ω) | ε (V) | I (A) |
|---|---|---|---|---|---|---|---|---|
| 1 | 0.35 | 0.50 | 12 | 90 | 1 | 2.5 | 2.10 | 0.84 |
| 2 | 0.12 | 0.80 | 6 | 60 | 1 | 10 | 0.50 | 0.05 |
| 3 | 0.50 | 0.20 | 3 | 90 | 50 | 100 | 15.00 | 0.15 |
| 4 | 0.00005 | 1.00 | 30 | 90 | 1 | — | 0.0015 | — |
Examples assume ε = N·B·L·v·sin(θ). Current values use I = ε/R when resistance is given.
Motional EMF in Moving Conductors
Motional emf is generated when a conductor moves through a magnetic field and charges are driven by the magnetic force. This calculator models the magnitude using ε = N·B·L·v·sin(θ) and, when a resistance is provided, estimates current and power.
1. What Motional EMF Represents
Motional emf is the induced potential difference along a moving conductor. It is the voltage available at the terminals before connecting a load. In sliding-rod demonstrations, it appears across the rod ends and can drive current in a complete circuit.
2. Inputs and Units You Should Verify
Check that B is in tesla, L is the effective length in meters, and v is in meters per second. θ is the angle between the velocity vector and the magnetic field; use degrees or radians consistently. N scales the result for multiple identical segments.
3. Typical Ranges in Labs and Industry
Earth’s magnetic field is about 25–65 μT, while small permanent magnets can reach roughly 0.1–1 T near their surfaces. Hand-driven motion may be 0.1–5 m/s; motors can exceed 10 m/s. These ranges help sanity-check outputs.
4. Why Angle and Effective Length Matter
The sine term captures geometry. If motion is parallel to the field (θ≈0°), the conductor does not cut field lines and emf approaches zero. If motion is perpendicular (θ≈90°), emf is maximized. Use the portion of conductor actually within the field.
5. Multiple Turns and Repeated Segments
For coils, N can represent turns, and the total emf scales approximately linearly when each turn experiences similar B, L, and v. In practice, nonuniform fields and varying radii reduce perfect scaling, so treat N as an effective value for real devices.
6. Load Resistance, Current, and Heating
Connecting a load turns voltage into current: I≈ε/R. Power dissipated as heat is P≈ε²/R for a resistive load. Low resistance can cause large currents, heating, and magnetic braking forces. Use realistic R and consider temperature-dependent resistance for better estimates.
7. Direction, Polarity, and Lenz’s Law
The calculator reports magnitude; polarity depends on motion direction, field direction, and conductor orientation. Apply the right-hand rule for v×B and Lenz’s law: the induced current opposes the change that produced it. This matters for generators and eddy-current brakes.
For best results, keep units consistent, use the effective length inside the field, and measure θ with a clear reference. Compare the calculated emf to multimeter readings under open-circuit conditions, then add R to model loaded operation and power.
Frequently Asked Questions
1. Is motional emf the same as transformer emf?
No. Motional emf comes from conductor motion through a magnetic field. Transformer emf comes from a changing magnetic flux through a stationary loop. Both are consistent with Faraday’s law, but the physical setups differ.
2. What should I use for θ in the formula?
Use the angle between the velocity direction and the magnetic field direction. If motion is perpendicular to the field, θ = 90° and sin(θ) = 1. If motion is parallel, θ = 0° and emf is near zero.
3. Why does the calculator ask for effective length L?
Only the part of the conductor that cuts magnetic field lines contributes to the induced voltage. If the field exists over a limited region, use the length that lies within that region rather than the full conductor length.
4. How does the number of turns N affect the result?
If each turn experiences similar field and motion, emf scales roughly linearly with N. In nonuniform fields or coils with varying radii, scaling is weaker, so treat N as an effective multiplier based on geometry.
5. When is the current estimate I = ε/R valid?
It is a simple resistive approximation for a closed circuit with total resistance R. Real systems may include internal resistance, contact resistance, and inductive effects, which can reduce or delay current compared to this estimate.
6. Can this calculator be used for a rail-and-slider generator?
Yes. Set L to the rail separation, choose B for the field in the gap, set v to the slider speed, and use θ = 90° if motion is perpendicular to the field. Add R to estimate current and power.
7. What are common causes of unexpected results?
Incorrect units, using full length instead of effective length, wrong θ reference, nonuniform magnetic fields, and ignoring additional circuit resistance are common. Also note that multimeter readings change under load compared to open-circuit voltage.
Practical Notes
- Use the effective length that actually cuts magnetic field lines.
- For maximum emf, motion should be perpendicular to the field (θ ≈ 90°).
- Direction (polarity) follows the right-hand rule and Lenz’s law.
- At very high speeds or strong fields, heating and forces can matter.