Magnetic Fields and Electromagnetism – Lecture 22 May 2025

Vocabulary flashcards summarizing key terms and definitions from the lecture on magnetic fields, magnetostatics, and electromagnetic induction.

Lorentz Force

Total force on a charged particle moving in electric and magnetic fields: F = q(E + v × B).

Electric Field (E) – Operational Definition

A field where a charge q experiences a force F = q E.

Magnetic Field (B) – Operational Definition

A field where a moving charge q with velocity v experiences a force F = q v × B.

Magnetic Permeability of Vacuum (μ₀)

Fundamental constant describing the ability of free space to transmit magnetic fields; μ₀ = 4π × 10⁻⁷ H/m.

Current (I)

Rate of flow of electric charge that generates magnetic fields when charges move.

Ampère-Laplace Law

Differential form giving the magnetic field contribution dB from an infinitesimal current element I dl: dB = (μ₀/4π)(I dl × r̂)/r².

Biot–Savart Law

Integral form for B at a point from a continuous current: B = (μ₀/4π)∮(I dl × r̂)/r².

Ampère’s Circuital Law

The line integral of B around a closed path equals μ₀ times the net current enclosed: ∮B·dl = μ₀I_enc.

Magnetic Field of an Infinite Straight Wire

Magnitude B = μ₀I/(2πr), circling the wire according to the right-hand rule.

Magnetic Field on the Axis of a Circular Loop

B = (μ₀I a²)/(2(a² + x²)^{3/2}), where a is loop radius and x is axial distance.

Magnetic Field at Center of a Circular Loop

Special case x = 0: B_center = μ₀I/(2a).

Solenoid (Ideal)

Long coil with N turns over length l producing nearly uniform internal field B = μ₀(N/l)I.

Solenoidal Field

Vector field with zero divergence; for magnetism ∇·B = 0 implies closed field lines.

Magnetic Flux (Φ_B)

Surface integral of B through area S: ΦB = ∬S B·dA, measured in Webers (Wb).

Weber (Wb)

SI unit of magnetic flux; 1 Wb = 1 T·m².

Tesla (T)

SI unit of magnetic flux density; 1 T = 1 Wb/m².

Gauss’s Law for Magnetism

Net magnetic flux through any closed surface is zero: ∬_S B·dA = 0 (no magnetic monopoles).

Gauss’s Law for Electricity

Electric flux through a closed surface equals enclosed charge over ε₀: ∬S E·dA = Qenc/ε₀.

Maxwell’s Equations (Electro-/Magnetostatics)

Set of four relations: Gauss-E, Gauss-B, ∮E·dl = 0, and ∮B·dl = μ₀I_enc.

Conservative Field

A field with zero curl (∮E·dl = 0); electric field in electrostatics is conservative, magnetic field is not.

Magnetic Monopole

Hypothetical isolated north or south pole; none have been observed, consistent with ∇·B = 0.

Static Magnetic Field

Time-independent B produced by steady currents; described by magnetostatics.

Time-Varying Magnetic Field

B that changes with time, able to induce electric fields per Faraday-Henry law.

Faraday-Henry Law (Electromagnetic Induction)

Changing magnetic flux through a circuit induces emf: emf = −dΦ_B/dt, with sign given by Lenz’s law.

Electromotive Force (emf)

Work per unit charge done around a closed path by non-electrostatic forces; source of induced current.

Lenz’s Law

Induced currents or emfs oppose the change in magnetic flux that produces them (negative sign in Faraday’s law).

Induced Current

Current that appears in a closed circuit due to a time-varying magnetic field, direction set by Lenz’s law.

Right-Hand Rule

Orientation convention where thumb points along current (or motion) and curled fingers show B direction.

Closed Field Lines

Magnetic field lines form continuous loops; they never start or end in space because ∇·B = 0.

Flux Linkage

Product of magnetic flux and number of turns N in a coil; relevant for induced emf: emf = −d(NΦ_B)/dt.