## 20.3 MUTUAL INDUCTANCE AND SELF-INDUCTANCE This section explores two related electromagnetic phenomena: self-induction, where a coil induces an electromotive force (emf) in itself, and mutual induction, where a changing current in one coil induces an emf in a nearby coil. ### Self-Induction **Definition:** The phenomenon in which a changing current in a coil induces an electromotive force (emf) in the coil itself. **Mechanism:** A change in current ($\Delta I$) within a coil over a time interval ($\Delta t$) causes a change in the magnetic field and thus a change in magnetic flux through the coil. This changing flux induces an opposing emf ($\varepsilon_L$) in the same coil. **Back EMF:** The self-induced emf is often called "back emf" because, according to Lenz's law, it always opposes the change in current that created it. **Inductors:** Coils designed to have a specific self-inductance are called **inductors** or **chokes**. They are fundamental components in AC circuits, where they function to control current flow. ### Mutual Induction **Definition:** The phenomenon in which a changing current in one coil (the primary coil) induces an emf in a neighboring coil (the secondary coil). **Mechanism:** When an alternating or changing current flows through the primary coil, it produces a changing magnetic flux. If a secondary coil is placed nearby, this changing flux links with it, inducing an emf in the secondary coil. The induced emf in the secondary coil ($\varepsilon_2$) is proportional to the rate of change of current in the primary coil ($\Delta I_1 / \Delta t$). ## Formulas and Units ### Self-Inductance The self-induced emf in a coil is given by: $$\varepsilon_L = -L \frac{\Delta I}{\Delta t}$$ Where: - $\varepsilon_L$ = self-induced emf (V) - $L$ = self-inductance of the coil (H) - $\Delta I$ = change in current (A) - $\Delta t$ = time interval (s) The self-inductance $L$ is defined as: $$L = \frac{-\varepsilon_L}{\Delta I / \Delta t}$$ ### Mutual Inductance The induced emf in the secondary coil is given by: $$\varepsilon_2 = -M \frac{\Delta I_1}{\Delta t}$$ Where: - $\varepsilon_2$ = induced emf in secondary coil (V) - $M$ = mutual inductance between the two coils (H) - $\Delta I_1$ = change in current in primary coil (A) - $\Delta t$ = time interval (s) The mutual inductance $M$ is defined as: $$M = \frac{\varepsilon_2}{\Delta I_1 / \Delta t}$$ ### Unit The SI unit for both self-inductance and mutual inductance is the **henry (H)**. ## Factors Affecting Inductance The inductance of a coil depends on several physical factors: 1. The number of turns in the coil ($N$) 2. The cross-sectional area of the coil ($A$) 3. The length of the coil ($l$) 4. The type of core material (permeability $\mu$) 5. For mutual inductance, the distance and orientation between the two coils. **Real-World Application:** Inductance is a fundamental principle behind transformers, electric motors, generators, and various electronic filters and oscillators.

20.3 Mutual Inductance And Self Inductance | Alternating Current | Physics 12