Comprehensive Guide to Magnetic Interaction and Storage

Magnetic Flux

Measures the amount of magnetic field passing through a given area.

Flux Formula

Φ_B = ∫ B • dA = ∫ B cos(θ) dA.

Webers (Wb)

Unit of magnetic flux, 1 Wb = 1 T·m².

Gauss's Law for Magnetism

States that the net magnetic flux through any closed surface is zero.

Magnetic Monopoles

No isolated north or south poles exist; cutting a magnet results in smaller dipoles.

Inductance ($L$)

Measured in Henries (H), it represents a circuit element's opposition to current changes.

Self-Inductance Definition

L = (NΦB) / I, where N is the number of turns, ΦB is flux, and I is current.

Faraday's Law of Induction

States that a changing magnetic flux induces an electromotive force (EMF).

Back EMF

The EMF induced in an inductor that opposes the change in current.

Solenoid Inductance Formula

L_solenoid = (μ₀ N² A) / ℓ.

Toroid Inductance Formula

L_toroid = (μ₀ N² h) / (2π) ln(b/a).

Energy in Magnetic Field

Stored in an inductor as U_L = (1/2) L I².

Magnetic Energy Density

Energy stored per unit volume in a magnetic field, u_B = (B²) / (2μ₀).

Capacitor vs. Inductor

Capacitors store charge/energy, while inductors store magnetic flux/energy.

Inductor Behavior

Opposes change in current; represents a time delay in current response.

Power in Inductor

P = I |EMF| = I (L dI/dt), representing power required to overcome back EMF.

Induction and Resistance

Inductors provide reactive resistance in AC circuits.

Current Changes in Inductor

Inductors resist instantaneous changes in current.

Inductance Dependence

Inductance is a geometric property dependent on shape, size, and material.

Induced EMF Formula

EMF_L = -L (dI/dt), relating inductance to current change rate.

Electric vs. Magnetic Energy Storage

Capacitors store energy in electric fields; inductors store energy in magnetic fields.

Units of Inductance

Inductance is measured in Henries (H), where 1 H = 1 Wb/A.

Equation of Motion for Inductors

Lenz's Law states induced EMF opposes the change causing it.

Induced EMF and Circuit Analysis

Understanding inductive response is key for analyzing AC circuits.

Common Mistake: Flux Linkage

Mistake: Confusing flux with flux linkage; L = NΦ_B / I.

Common Mistake: Angle in Flux Calculation

Mistake: Using incorrect angle; θ is between B-field and normal vector.

Common Mistake: Invariance of Inductance

Thinking L changes with current; L remains constant for standard materials.

Common Mistake: Uniform Field Assumption

Assuming Φ = BA in cases where B is not uniform requires integration.