Electromagnetic induction
Faraday's law can look like a lot of symbols until you watch it happen. So change how fast the field is changing and see the induced EMF and current respond — with the direction always fixed by Lenz's law: the induced current opposes the change that caused it.
The rules you're seeing
Faraday's law
EMF = −N·dΦ/dt. An EMF is induced whenever the magnetic flux through a coil changes — by changing B, changing the area, or changing the angle. This simulator changes B.
Lenz's law
The minus sign isn't just bookkeeping — it says the induced current always opposes the change that caused it. That's really conservation of energy in disguise: you must do work to change the flux against the opposition.
No change, no current
A magnetic field that is present but not changing induces absolutely nothing. It's the rate of change dB/dt (or dΦ/dt) that matters, not the field strength itself.
More turns, more EMF
EMF ∝ N. Doubling the number of turns doubles the induced EMF for the same rate of flux change — why induction coils and transformers use many turns of wire.
Part of the Electromagnetic Induction chapter — read the notes, grab the formula sheet and take the quiz. One of Priodemy for School, free with every EduSuite school.
Change is the whole story
Flux, and why it has three ways to change
Magnetic flux is Φ = BA cos θ — the field strength, the area it passes through, and the angle between the field and the normal to that area. Faraday's law says the induced EMF is ε = −N dΦ/dt: the rate at which that flux changes, multiplied by the number of turns.
Because flux is a product of three things, there are three distinct ways to induce an EMF, and exam questions use all of them. You can change B by moving a magnet closer or switching a nearby current on and off. You can change A by stretching, squashing or sliding a loop out of the field. Or you can change θ by rotating the coil, which is exactly what a generator does. Recognising which of the three a question is describing is usually the whole difficulty.
The minus sign is Lenz's law
The negative sign in Faraday's law is not bookkeeping — it is a physical statement. The induced current always flows in the direction that opposes the change producing it. Push a magnet's north pole towards a coil and the coil's near face becomes a north pole, repelling it. Pull the magnet away and the face becomes a south pole, trying to hold it back. Either way, you have to do work against the opposition, and that work is where the electrical energy comes from.
This is conservation of energy expressed as a direction rule. If the induced current helped the change instead of opposing it, the motion would accelerate on its own and generate ever more energy from nothing. Lenz's law is the reason that cannot happen, and questions that ask "why is there a minus sign" are asking for exactly that argument.
No change, no current
A magnet held stationary inside a coil, however strong, induces nothing. The flux is large but constant, so dΦ/dt is zero. This catches people out because it feels as though a strong field ought to do something. What matters is not the flux but its rate of change — and a fast, small change produces a bigger EMF than a slow, large one.
Mistakes that cost marks
Confusing EMF with current. Faraday's law gives the induced EMF. The current only follows if the circuit is complete, and its size then depends on the resistance through I = ε/R. An open loop can have a perfectly good induced EMF and no current at all.
Treating N as part of the flux. The number of turns multiplies the EMF, not the flux through a single turn. Writing Φ = NBA and then also multiplying by N in Faraday's law double-counts the coil.
Getting the induced direction backwards. Decide first whether the flux is increasing or decreasing, then choose the current that opposes that change — not the field itself. When flux is decreasing, the induced current supports the existing field rather than fighting it.