Self Inductance — Revision Notes

⚡ 30-Second Revision

Magnetic Flux Linkage: — $Phi = LI$
Self-Inductance: — $L = \frac{Phi}{I}$ (Unit: Henry, H)
Induced EMF: — $E = -L \frac{dI}{dt}$ (Lenz's Law)
Energy Stored: — $U = \frac{1}{2}LI^2$
Solenoid Inductance: — $L = \frac{mu N^2 A}{l} = mu n^2 A l$
Lenz's Law: — Induced EMF opposes the *change* in current.

2-Minute Revision

Self-inductance ($L$) is a coil's inherent property to oppose changes in current flowing through it. This opposition arises from a self-induced EMF ($E$) generated within the coil itself, as per Faraday's and Lenz's laws.

The magnetic flux ($Phi$) linking the coil is directly proportional to the current ($I$), with $L$ as the constant of proportionality: $Phi = LI$. The induced EMF is given by $E = -L \frac{dI}{dt}$, where the negative sign signifies opposition to the current change.

An inductor stores energy in its magnetic field, quantified by $U = \frac{1}{2}LI^2$. For a solenoid, $L = \frac{mu N^2 A}{l}$, showing dependence on geometry (N, A, l) and core material permeability ($mu$), but not on the current.

Remember to convert units (mH to H) and apply Lenz's law correctly for direction-based questions.

5-Minute Revision

Self-inductance is the 'electrical inertia' of a coil, resisting changes in its own current. When current ($I$) flows, it creates magnetic flux ($Phi$) through the coil, where $Phi = LI$. If $I$ changes, $Phi$ changes, inducing an EMF ($E = -L \frac{dI}{dt}$) in the coil itself.

The negative sign is crucial, indicating that $E$ opposes the *change* in $I$ (Lenz's Law). For example, if $I$ increases, $E$ acts to decrease it; if $I$ decreases, $E$ acts to increase it. The unit of $L$ is the Henry (H).

An inductor stores energy in its magnetic field, $U = \frac{1}{2}LI^2$. For a solenoid, $L = \frac{mu N^2 A}{l}$, where $N$ is turns, $A$ is area, $l$ is length, and $mu$ is core permeability. This formula highlights that $L$ depends on geometry and material, not current.

Key points for NEET: 1. Apply formulas correctly, paying attention to units (mH to H). 2. Understand Lenz's Law for direction of induced EMF. 3. Know factors affecting $L$. 4. Be aware that current cannot change instantaneously in an inductor.

Prelims Revision Notes

Self-Inductance (L)

Definition: — Property of a coil to oppose changes in current flowing through it by inducing an EMF in itself.
Magnetic Flux Linkage: — $Phi = LI$

* $Phi$: Magnetic flux linkage (Weber, Wb) * $L$: Self-inductance (Henry, H) * $I$: Current (Ampere, A)

Induced EMF: — $E = -L \frac{dI}{dt}$

* Negative sign indicates opposition to change in current (Lenz's Law). * If current increases ($rac{dI}{dt} > 0$), $E$ opposes current. If current decreases ($rac{dI}{dt} < 0$), $E$ supports current.

Energy Stored in Inductor: — $U = \frac{1}{2}LI^2$

* Energy is stored in the magnetic field.

Self-Inductance of a Solenoid: — $L = \frac{mu N^2 A}{l} = mu n^2 A l$

* $mu = mu_0 mu_r$: Permeability of core material ($mu_0 = 4pi \times 10^{-7},\text{T m/A}$ for air/vacuum) * $N$: Total number of turns * $n = N/l$: Number of turns per unit length * $A$: Cross-sectional area * $l$: Length of solenoid

Factors Affecting L: — Geometry (N, A, l) and core material ($mu$). Independent of current.
Important Note: — Current cannot change instantaneously in an inductor ($dI/dt$ would be infinite, leading to infinite EMF).

Vyyuha Quick Recall

To remember the key formulas for self-inductance, think of 'LIFe is HALF LI SQUARED':

LIFe: — $Phi = LI$ (Flux = L * Current)
e is L di/dt: — $E = -L \frac{dI}{dt}$ (EMF = -L * rate of change of current)
HALF LI SQUARED: — $U = \frac{1}{2}LI^2$ (Energy = 1/2 * L * Current squared)

For solenoid inductance, remember 'L is Mu N Squared A over L' (where 'L' is length):

$L = \frac{mu N^2 A}{l}$