Mutual Inductance EMF

\mathcal{E} = -M\frac{dI}{dt}

EMF induced in one coil due to changing current in another.

Variables

Induced EMF

EMF in secondary coil

In SI units: kg·m²/(A·s³)

Mutual inductance

In SI units: kg·m²/(A²·s²)

dI/dt

Current rate

Rate of current change in primary

A/s

Derivation

ε₂ = -dΦ₂₁/dt = -M(dI₁/dt) where Φ₂₁ = MI₁.

Your notes

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Other electricity & magnetism formulas with the same quantities

Motional EMF (Electromagnetic Induction) shares Induced EMF

Where this formula is listed

Electricity & Magnetism formulas, under Electromagnetic Induction, alongside Magnetic Flux, Inductor Energy and RL Time Constant.
In the electricity & magnetism list it comes after RL Time Constant and before Transformer Equation.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Mutual Inductance EMF formula?

Mutual Inductance EMF is written ℰ = −M(dI/dt). EMF induced in one coil due to changing current in another. It belongs to Electricity & Magnetism, under Electromagnetic Induction.

What are the units in ℰ = −M(dI/dt)?

In SI units, ε is induced emf, measured in kg·m²/(A·s³); M is mutual inductance, measured in kg·m²/(A²·s²); dI/dt is current rate, measured in A/s.

How is the Mutual Inductance EMF formula derived?

ε₂ = -dΦ₂₁/dt = -M(dI₁/dt) where Φ₂₁ = MI₁. The result is ℰ = −M(dI/dt).