Mutual Inductance

How to Use

• Current slider — set the peak current in Coil 1 (0–1 A).
• Separation slider — move the coils apart; coupling decreases with distance.
• Alignment slider — misalign the coils vertically; coupling drops as coils shift off-axis.
• Iron Core toggle — switch between air core and iron core; iron dramatically increases coupling.
• Start / Stop — pause the animation to inspect a moment in time.

What to Observe

• Animated field lines show energy linking from Coil 1 to Coil 2.
• \(V_2\) spikes when \(dI_1/dt\) is highest (at the zero crossing of current).
• Coupling coefficient \(k\) updates in real time as you change geometry and core material.
• Iron core raises \(k\) toward 1, approaching an ideal transformer.

Key Equations

\[M = k\sqrt{L_1 L_2}\]

\[V_2 = M \frac{dI_1}{dt}\]

\[k = \frac{M}{\sqrt{L_1 L_2}} \quad (0 \leq k \leq 1)\]