Lenz's Law: Which Way Does the Current Go?

Slide the magnet along the axis of the coil: the flux through the coil changes, so a current is induced — and it always runs the way that fights the change, which is the minus sign in emf = -N dPhi/dt. Read the induced EMF with its sign, which way the current runs seen from the right-hand end of the axis, the pole the coil turns towards the magnet, and the force, which never helps the motion. A magnet held still induces nothing, however strong it is.

Induced current-26.98 mA
Flux per turn22.479 µWbflux through one turn
Flux linkage4.4959 mWbflux linkage, N times the flux
Slope of the linkage0.2698 Wb/mhow fast the linkage changes with position
Power dissipated7.28 mWheat in the circuit
Where the EMF peaks± 10.0 mmwhere the EMF peaks: half a coil radius

What Lenz's law says hereThe flux through the coil points right and is growing as the magnet moves in. The induced current runs clockwise seen from the right, turning the coil's near face into a north pole that repels the magnet.

Energy checkMechanical power in: 7.28 mW. Electrical power out: 7.28 mW. Lenz's law is energy conservation.

What to noticeThis is the peak: the EMF is largest at half a coil radius from the centre, not at the centre itself.

The model: a point dipole of 1.00 A·m2 on the axis of a coil of radius 20.0 mm with coincident turns, in a circuit of pure resistance — no self-inductance, and no figure here is a measurement. The force arrow is not drawn to scale: its length is on a square-root scale, because the force spans seven decades across these sliders. The motion arrow is proportional to the speed.
Induced EMF  emf = -N dPhi/dt
-269.75 mV
induced EMF, sign and all
Which way the current runs
clockwise, seen from the right
which way the induced current runs
The coil's near face
the coil's near face is a north pole
the face the magnet is nearest
Force on the magnet  F = m I dG/dz
7.28 mN
it repels the magnet, slowing the approach
Magnet position-10 mm
0 mm is the coil's centre; its radius is 20.0 mm
Magnet velocity1.0 m/s
positive is to the right; 0.0 m/s induces nothing
Turns on the coil200 turns
Circuit resistance10.0 Ω
The magnet itself
the magnet's north end points right
Load a case
custom setting
Tip: load a case, then press Flip twice — every sign reverses and comes back, and the force never moves.