Faraday's Law tells you how big the emf is. Lenz's law tells you which way the induced current flows. You will need the right-hand rule for loops from Fields of Wires and Solenoids: curl your fingers along the current and your thumb points along the field it makes inside the loop.
Key idea
The induced current flows so that its own field opposes the change in flux. If the flux through a loop is growing, the induced field points against it. If the flux is shrinking, the induced field points the same way, trying to keep it.
- Which way does the outside field point through the loop?
- Is the flux through the loop growing or shrinking?
- Growing: the induced field points the opposite way. Shrinking: the induced field points the same way.
- Point your right thumb along the induced field; your fingers curl along the induced current.
Why it works
Suppose the induced current helped the change instead. Push a magnet toward a coil, and the coil would pull it in faster, which would make more current, which would pull harder: energy from nothing. Opposing the change is what energy conservation demands. You do work pushing the magnet against the coil's push, and that work becomes the electrical energy.
Common mistake
Thinking the induced field always points against the magnet's field. It opposes the change. When a magnet is pulled away and the flux drops, the induced field points the same way as the magnet's field, trying to keep the flux up. Check: ask "growing or shrinking?" before anything else.
Worked example: A field into the page, growing
A loop lies in the page. A field into the page grows stronger. Which way does the induced current flow, as you look at the page?
- The flux into the page is growing.
- So the induced field must point out of the page inside the loop.
- Thumb out of the page: your fingers curl counterclockwise.
Answer: Counterclockwise
Worked example: Pulling a magnet away
The north pole of a bar magnet faces a loop from the left and is pulled away to the left. Looking at the loop from the magnet's side, which way does the current flow?
- Field lines leave the north pole, so the magnet's field through the loop points to the right, away from you.
- Pulling the magnet away makes that flux shrink.
- To keep it, the induced field points the same way: to the right, away from you.
- Thumb pointing away from you: your fingers curl clockwise, as you see it.
Answer: Clockwise, as seen from the magnet. The loop's near face acts like a south pole and pulls back on the magnet.