Lenz's Law and the Minus Sign

Faraday's law tells you the size of an induced EMF: EMF = -d(Phi)/dt. The minus sign is Lenz's law in disguise. It says the induced current fights the change in flux through the loop, not the flux itself. If flux is increasing, the induced current creates its own magnetic field pointing opposite to that increase. If flux is decreasing, the induced current creates a field pointing along the original direction, trying to prop it up. Either way the loop acts like it resents change.

To pick a direction, do three steps. First, decide how the flux through the loop is changing: growing or shrinking, and in which direction it points. Second, figure out what magnetic field the induced current needs to make to oppose that change. Third, use the right-hand rule in reverse: curl your fingers the way current would need to flow to produce that opposing field, and your fingers show the current's direction around the loop.

This is why the magnet falling through a copper pipe drifts down lazily instead of free-falling. As it falls, the changing flux drives eddy currents in the pipe wall, and those currents create a field that pushes back on the magnet, converting its kinetic energy into heat. That same opposition is what makes generators feel harder to crank as you draw more current from them, and it sets up the energy bookkeeping behind inductors and RL circuits, where an inductor's back-EMF resists any change in current flowing through it.