Lenz’s Law
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 4 practice questions.
Lenz’s law gives the direction: the induced current flows so its own field opposes the change in flux. It’s the minus sign in Faraday’s law, and it’s energy conservation: induction always pushes back against whatever causes it.
1. Finding the direction
Step 1. Which way does the original field point through the loop?
Step 2. Is that flux increasing or decreasing?
Step 3. Increasing → induced B points the opposite way. Decreasing → induced B points the same way.
Step 4. Right-hand rule: curl fingers with the current so your thumb points along the induced B.
2. Forces from Lenz’s law
The induced current always produces a force that resists the motion causing it: approaching magnets are pushed back, departing ones pulled back.
That’s why you must do work to move a magnet near a coil, and why that work shows up as electrical energy.
Eddy currents in solid metal do the same thing: they slow a magnet falling through a pipe, brake trains, and damp a swinging metal plate.
No change in flux (a loop fully inside a uniform field, moving steadily): no current, no force.
3. Example, then try it
A loop lies flat on the page in a field pointing into the page. The field is getting weaker. Which way does the induced current flow?
Flux into the page is decreasing, so the induced field points into the page to make up for it.
Curling fingers so the thumb points into the page gives clockwise current.
A rectangular loop is pulled to the right at steady speed, out of a region where B points into the page. Its left side is still inside the field. Find the direction of the induced current and the magnetic force on the loop.
Flux: into the page, and decreasing as less of the loop stays in the field.
Induced B: into the page (same direction, to oppose the decrease), so the current is clockwise.
Left side: clockwise means the current goes up on the left side. F = IL × B = (up) × (into) points left.
Meaning: the force opposes the pull. You must keep pulling to keep the loop moving.
Answer: clockwise; the force on the loop points left, against its motion.
4. Common mistakes
A metal ring rests on top of a coil, around its core. A switch turns on a current in the coil. What does the ring do?
The coil’s flux through the ring suddenly increases. The ring’s induced current makes an opposing field, so the ring and coil repel: the ring jumps.
Ready to practice?
4 questions on Lenz’s Law, each with a hint and an explanation for every wrong answer.