AP® Physics C: Electricity and Magnetism · Unit 13 · Topic 13.3

Induced Current and the Force That Fights You

When you drag a conducting loop through a magnetic field, the induced current it carries always creates a force that pushes back against your motion. That retarding force is what you feel as resistance, and it's the price of making electrical energy.

Pull a loop out of a magnetic field and flux through it drops. That induces a current. But that current sits in a magnetic field too, so the field exerts a force on it — F = IL x B. Work out the direction with Lenz's law: the induced current always flows the way that opposes the change causing it. Here that means the force on the current-carrying loop points back, against the motion pulling it out. You feel this as a drag, a stiffness in your hand, even though nothing is touching the loop.

This is why a generator gets harder to turn the instant you connect a load. With no circuit closed, no current flows, so there's no opposing force — just friction. Close the circuit and current flows, and now every bit of that current fights the rotation. The more current you draw, the harder you have to push or turn. You can't get something for nothing: the electrical energy delivered to the load has to come from somewhere, and that somewhere is the mechanical work you put in against the opposing force.

This connects directly to the energy bookkeeping for the whole unit. The retarding force times the distance moved equals the work you do, and that work converts exactly into the electrical energy dissipated in the resistance. Lenz's law isn't just a direction rule — it's energy conservation wearing a magnetic disguise, and it sets up the motional EMF and power calculations that follow.

Key terms

Lenz's law
The induced current flows in the direction that opposes the change in magnetic flux causing it.
Motional EMF
The voltage induced in a conductor moving through a magnetic field, equal to BLv for a loop of width L.
Retarding force
The force on the induced current from the magnetic field, always directed to oppose the conductor's motion.
Magnetic flux
The amount of magnetic field passing through a loop's area, equal to B times area times the cosine of the angle between them.

Watch it explained

  1. How it worksHow does the induced current in a moving loop create a force that opposes the motion?
  2. Worked exampleFind the force needed to drag a loop out of a field at steady speed against its own current.
  3. Common mistakeWhy doesn't the induced current ever end up helping to push the loop along?
  4. Ties togetherHow does that opposing force explain where a generator's electrical energy comes from?

Check yourself

Your turn1 of 2
Find the force needed to drag a 22 cm wide loop out of a 0.684 tesla field at a steady 4.7 m/s, against the current induced in its 6 ohm resistance.

End of topic.