Lentz's Law Direction Predictor

Physics Electricity and Magnetism • Electromagnetic Induction and Inductance

Written by STEM Calculators Team Published January 18, 2026 Updated February 24, 2026

3. Lenz’s Law Direction Predictor

Predicts the direction of induced current/EMF using $\varepsilon=-\,d\Phi_B/dt$ and the right-hand rule. Use a scenario (changing uniform $B$ or a moving magnet) and the diagram will show the induced direction.

Convention: ⊙ is out of the screen (+$\hat{z}$, positive flux), ⊗ is into the screen (−$\hat{z}$, negative flux). Inputs accept 1e-3, pi, sqrt(2), sin(), cos(), tan(), ln(), log(), abs(). Use * for multiplication.

Inputs

Scenario

Choose scenario:

Both scenarios output induced $\mathbf{B}_{\text{ind}}$ and current direction (CW/CCW).

Magnet → loop

Pole facing the loop:

In this model: N facing loop produces flux ⊙ through the loop; S facing produces ⊗.

Motion:

If you drag the magnet, motion is detected live (and overrides this while dragging/playing).

Distance $d$ (m):

Controls flux magnitude (qualitative) $\propto 1/d^2$. Drag the magnet in the diagram too.

Flux scale $k$ (Wb·m$^2$):

Used only to display a flux magnitude estimate: $|\Phi|\approx k/d^2$.

Changing uniform $B$

External $B$ direction:

Sets the sign of flux $\Phi_B$.

What is happening?

This is the sign of $d\Phi_B/dt$ given the chosen direction.

Loop area $A$ (m$^2$):

Optional, used to show a numeric flux change if you provide $\Delta B$ and $\Delta t$.

Change $\Delta B$ (T):

Optional magnitude (used only for a sample $\Delta\Phi$, not required for direction).

$\Delta t$ (s):

Optional time interval (used only to show $\varepsilon_{\text{avg}}$).

Visual controls

Line density (visual):

Scales dot/cross density in the loop.

Show guides:

Shows labels and $\theta$-style annotations.

Pan/zoom: drag to pan • mouse wheel / trackpad / pinch to zoom • “Reset view” restores default.
Drag the magnet (in magnet scenario) to see direction flip between approach/retreat.

Ready

Steps

Enter values and click Solve.

Direction diagram

Loop, flux change, induced field, and induced current direction

Legend

Loop (in the $x$-$y$ plane)
External flux through loop (⊙ out / ⊗ in)
Induced field $\mathbf{B}_{\text{ind}}$ (opposes the change)
Induced current direction (CW / CCW by right-hand rule)
Magnet (drag to change distance in magnet scenario)

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3. Lenz’s Law Direction Predictor — Theory

Lenz’s law gives the direction of the induced EMF/current: the induced current always flows so that the magnetic field it creates opposes the change in magnetic flux through the loop.

Magnetic flux sign convention

We take the loop to lie in the $x$-$y$ plane. Its area normal is $\hat{\mathbf{n}}=+\hat{\mathbf{z}}$ (out of the screen).

Field out of the screen ($+\hat{z}$) is shown as ⊙ and taken as $\Phi_B>0$.
Field into the screen ($-\hat{z}$) is shown as ⊗ and taken as $\Phi_B<0$.

Lenz’s law in one line

If the external flux is changing, the induced flux tries to cancel that change:

\varepsilon = -\,\frac{d\Phi_B}{dt} \quad\Rightarrow\quad \text{induced } \mathbf{B}_{\text{ind}} \text{ points opposite the change in } \Phi_B.

Right-hand rule: induced field ↔ current direction

Once you know the direction of $\mathbf{B}_{\text{ind}}$, use the right-hand rule for a current loop:

$\mathbf{B}_{\text{ind}}$ out of screen (⊙) ⇔ induced current is counterclockwise (CCW).
$\mathbf{B}_{\text{ind}}$ into screen (⊗) ⇔ induced current is clockwise (CW).

Classic scenario: magnet approaching a loop

As a magnet gets closer, the magnitude of flux through the loop increases. The loop responds by producing a field that opposes that increase.

N pole approaching (as modeled here): external flux through the loop increases out of screen ⇒ induced field into screen ⇒ induced current CW.
N pole retreating: external flux out of screen decreases ⇒ induced field out of screen ⇒ induced current CCW.
Swap directions if the S pole faces the loop.

Common pitfalls

Lenz’s law opposes the change, not the field itself.
Be consistent about which direction is “positive” flux (we use ⊙ as positive).
If the motion reverses (approach ↔ retreat), the induced current direction flips.