Question

Define mutual inductance of a pair of coils. Write its SI unit.

Hint:

Definitions in physics board exams often carry marks split into the theoretical statement and the mathematical formula. Providing both ensures you definitively secure full marks.

Answer 1

Concept:
• Mutual inductance fundamentally characterizes the electromagnetic interaction specifically existing between two distinct, magnetically coupled coils.
• When a dynamically changing electric current passes strictly through one coil, it actively generates a changing magnetic flux that subsequently links with the neighboring second coil, directly inducing an electromotive force (EMF) inside it.

Step 1: State the formal definition
The mutual inductance of a pair of physically coupled coils is formally defined as the total magnetic flux mathematically linked with one coil when a steady unit electric current (1 Ampere) actively flows through the other neighboring coil.
Alternatively, it can be rigorously defined based on Faraday's law: it is mathematically equal to the magnitude of the induced electromotive force (EMF) generated in the secondary coil when the active current running through the primary coil changes precisely at a unitary rate of $1 \text{ Ampere per second}$.
Mathematically, $\Phi_{21} = M_{21} I_1$ or $|e_2| = M_{21} \left| \frac{dI_1}{dt} \right|$.

Step 2: Provide the SI unit
The standard SI unit for mutual inductance is the Henry (H).
It can also be dimensionally expressed as Weber per Ampere ($\text{Wb A}^{-1}$) or Volt-second per Ampere ($\text{V s A}^{-1}$).