What it does
When a metal rod moves through a magnetic field, the free charges in it move with it, and the field pushes them along the rod. That push is an emf, the motional emf: ε = B ℓ v, where B is the field, ℓ the length of the rod across the field, and v its speed. You can also see it as Faraday’s law: as the rod slides, the loop of rails, rod and resistor encloses more and more flux, at a rate of B ℓ v webers per second.
If the rails are joined by a resistor, a current I = ε/R flows. Now the field pushes on that current with a force F = B I ℓ, and (by Lenz’s law) always against the motion. So keeping the rod moving takes work, and that work turns into heat in the resistor.
This page shows the rod sliding through a field into the page, with the current and the drag force drawn as arrows. It has three ways to move the rod: at a steady speed (you push), push and let go (it slows down and stops), and a steady pull (it speeds up to a top speed where the drag equals the pull). A graph shows the speed against time.
It follows the electromagnetic induction chapter of Class 12 Physics (motional electromotive force, energy consideration, Lenz’s law). Before this, see a magnet and coil in faraday induction and the force on a current in fleming's rule; after it, try coils that induce emfs in each other in the inductance lab.
How to use it
- Choose how the rod moves: Steady speed, Push and let go or Steady pull.
- Set the field B (0.1 to 1 T), the rod length ℓ (10 to 100 cm) and the resistance R (1 to 10 Ω).
- Set the speed v (steady speed and push), the rod’s mass m (push and pull) or the pulling force (pull).
- Press Start to run the motion, Reset to go back to the start. Read the emf, current, force and power as it moves.
Worked example
The page opens with B = 0.5 T, ℓ = 50 cm, R = 2 Ω and the rod moving at a steady 4 m/s.
- ε = B ℓ v = 0.5 × 0.5 × 4 = 1 V.
- I = ε / R = 1 / 2 = 0.5 A, anticlockwise round the circuit.
- The drag force is F = B I ℓ = 0.5 × 0.5 × 0.5 = 0.125 N, so you must push with 0.125 N.
- The power you supply is F v = 0.5 W, and the heat in the resistor is I²R = 0.5 W: the same.
Choose Push and let go with m = 0.2 kg: the time constant is τ = mR / (B²ℓ²) = 0.2 × 2 / (0.25 × 0.25) = 6.4 s, and the 1.6 J of kinetic energy ends up as heat. With a Steady pull of 0.5 N the top speed is FR / (B²ℓ²) = 16 m/s.
Tips
- If the circuit is open (no resistor), the emf is still there but no current flows, so there is no drag.
- The drag grows with speed, which is why the rod never speeds up without limit under a steady pull.
- Eddy-current brakes in trains and some exercise bikes use exactly this drag.
FAQ
Which way does the current go? Use the right-hand rule, or Lenz’s law: the loop’s area and flux are growing, so the current flows to make a field that opposes the increase, which here means anticlockwise.
Is friction included? No. The rails are frictionless, so all the slowing comes from the magnetic drag.
Is anything saved? No. Everything is worked out on this page and nothing leaves your device.
Where the numbers come from
- Motional emf ε = Bℓv, current I = ε/R, force F = BIℓ = B²ℓ²v/R, power Fv = I²R, and the rod's speed v = v_t + (v₀ − v_t) e^(−t/τ) with τ = mR/(B²ℓ²) and v_t = FR/(B²ℓ²). Standard physics results (Newton's second law with the magnetic drag).
- Checked against an independent Python script that steps Newton's law numerically (fourth-order Runge-Kutta).
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.