Flashcards for Capacitance and Magnetic Fields

This set of flashcards covers key vocabulary and concepts from the lectures on Capacitance (Chapter 25) and Magnetic Fields (Chapters 28, 29, 30).

Capacitor

A device in which electrical energy can be stored, consisting of two isolated conductors (plates) with charges of equal magnitude but opposite signs.

Capacitance (C)

A measure of how much charge (q) must be put on the plates to produce a certain potential difference (V) between them, defined by q = CV. Its value depends only on the geometry of the plates.

Farad (F)

The SI unit of capacitance, equal to one coulomb per volt (1 C/V).

Parallel-Plate Capacitor

A capacitor consisting of two parallel conducting plates of area A separated by a distance d, with capacitance C = ε₀A/d.

Capacitors in Parallel

When connected in parallel, capacitors have the same potential difference (V). Their equivalent capacitance (Ceq) is the sum of individual capacitances: Ceq = ΣCj.

Capacitors in Series

When connected in series, capacitors have identical charge (q). The sum of potential differences across them equals the applied potential difference. Their equivalent capacitance (Ceq) is given by 1/Ceq = Σ(1/Cj).

Energy Stored in a Capacitor

The electric potential energy (U) stored in a charged capacitor, equal to the work required to charge it: U = q²/(2C) = (1/2)CV².

Energy Density (u)

The potential energy per unit volume stored in an electric field of magnitude E, given by u = (1/2)ε₀E².

Dielectric Constant (k)

A numerical factor by which the capacitance of a capacitor increases when the space between its plates is completely filled with an insulating material (dielectric). For a vacuum, k = 1.

Dielectric Strength

The maximum value of the electric field that a dielectric material can tolerate without breaking down (forming a conducting path).

Induced Charge

Charges that appear on the faces of a dielectric material when it is placed in an external electric field, opposing the external field and weakening it within the dielectric.

Electric Current (i)

The rate at which positive charge dq passes through a hypothetical plane in time dt, defined as i = dq/dt. The SI unit is the ampere (A).

Junction Rule (Kirchhoff's Current Law)

The sum of the currents entering any junction must be equal to the sum of the currents leaving that junction (conservation of charge).

Current Density (J)

A vector quantity that describes the flow of charge through a cross section of a conductor, representing the current per unit area. Its direction is the same as the velocity of positive moving charges.

Drift Speed (vd)

The average speed at which charge carriers (e.g., electrons) move in a conductor under the influence of an electric field, often much smaller than their random-motion speeds. Related to current density by J = (ne)vd.

Resistance (R)

A characteristic of a conductor that determines the current (i) resulting from a potential difference (V) applied between two points, defined as R = V/i. The SI unit is the ohm (Ω).

Resistivity (ρ)

A property of a material, defined as the ratio of the electric field magnitude (E) to the current density magnitude (J) within the material: ρ = E/J. The SI unit is the ohm-meter (Ω·m).

Conductivity (σ)

The reciprocal of resistivity, σ = 1/ρ.

Ohm's Law

An assertion that the current through a device is always directly proportional to the potential difference applied to the device (i.e., its resistance is independent of the magnitude and polarity of V).

Power in Electric Circuits (P)

The rate of energy transfer in an electrical device, given by P = iV. If the device is a resistor, P = i²R = V²/R (resistive dissipation).

Semiconductors

Materials that have few conduction electrons but can become conductors when doped with other atoms that contribute charge carriers.

Superconductors

Materials that lose all electrical resistance below a certain critical temperature.

Emf Device

A device that does work on charge carriers to maintain a potential difference between its terminals, providing an emf (work per unit charge).

Ideal Emf Device

An emf device that lacks internal resistance, so the potential difference between its terminals equals its emf.

Real Emf Device

An emf device that has internal resistance (r), so its terminal potential difference (V) is less than its emf (ε) when current (i) flows: V = ε - ir.

Loop Rule (Kirchhoff's Voltage Law)

The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero (conservation of energy).

Resistors in Series

When connected in series, resistors have identical currents. Their equivalent resistance (Req) is the sum of individual resistances: Req = ΣRj.

Resistors in Parallel

When connected in parallel, resistors have the same potential difference across them. Their equivalent resistance (Req) is given by 1/Req = Σ(1/Rj).

Ammeter

An instrument used to measure current, which must have very low resistance and be inserted in series with the current to be measured.

Voltmeter

An instrument used to measure potential differences (voltage), which must have very high resistance and be connected in parallel across the points whose potential difference is to be measured.

RC Circuit (Charging)

A circuit with a resistor R and capacitor C. When a constant emf ε is applied, the charge on the capacitor increases exponentially: q = Cε(1 - e^(-t/τC)), where τC = RC is the capacitive time constant.

RC Circuit (Discharging)

When a capacitor (initially with charge q₀) discharges through a resistor R, its charge decays exponentially: q = q₀e^(-t/τC).

Magnetic Field (B)

A vector quantity defined in terms of the magnetic force (FB) it exerts on a test particle of charge q moving with velocity v: FB = q(v × B). The SI unit is the tesla (T).

Magnetic Field Lines

Lines used to represent magnetic fields, where the tangent to a line gives the direction of B, and the spacing indicates the field's magnitude.

Magnetic Pole

The ends of a magnet where field lines emerge (north pole) or enter (south pole). Opposite poles attract, and like poles repel.

Crossed Fields

A region containing both a perpendicular electric field (E) and a magnetic field (B) that exert opposing forces on a charged particle. Used to balance forces and measure particle speed (v = E/B).

Hall Effect

The phenomenon where a potential difference (Hall potential V) is set up across a current-carrying conductor in a perpendicular magnetic field, due to the deflection of charge carriers. Used to determine the sign and density of charge carriers.

Charged Particle in Uniform Circular Motion

A charged particle moving with velocity v perpendicular to a uniform magnetic field B will travel in a circle of radius r = mv/(|q|B). The period of revolution is T = 2πm/(|q|B) and frequency f = |q|B/(2πm).

Helical Path

The path of a charged particle in a uniform magnetic field if its velocity has a component parallel to the field, in addition to the perpendicular component.

Cyclotron

A particle accelerator that uses electric forces to accelerate charged particles as they spiral outward in a magnetic field, timed by a resonance condition (f = fosc).

Magnetic Force on a Current-Carrying Wire

A straight wire of length L carrying current i in a uniform magnetic field B experiences a force FB = i(L × B). The force is perpendicular to both the current direction and the field.

Magnetic Dipole Moment (μ)

A vector property of a current-carrying coil (or other magnetic dipole), with magnitude μ = NiA (N = turns, i = current, A = area). Its direction is given by a right-hand rule and tends to align with an external magnetic field.

Torque on a Current Loop

A current-carrying coil with magnetic dipole moment μ in a uniform magnetic field B experiences a torque τ = μ × B.

Orientation Energy of a Magnetic Dipole (U)

The energy of a magnetic dipole μ in an external magnetic field B, dependent on its orientation: U = -μ ⋅ B.

Biot–Savart Law

A law describing the magnetic field dB produced by a current-length element ids at a point P located a distance r from the element: dB = (μ₀/4π) (ids × r̂)/r², where μ₀ is the permeability constant.

Magnetic Field of a Long Straight Wire

The magnitude of the magnetic field at a perpendicular distance R from a long straight wire carrying current i is B = μ₀i/(2πR). Field lines form concentric circles around the wire.

Magnetic Field of a Circular Arc

The magnitude of the magnetic field at the center of a circular arc of radius R and central angle φ (in radians) carrying current i is B = μ₀iφ/(4πR).

Ampere's Law

Relates the line integral of the magnetic field B around a closed loop (Amperian loop) to the net current ienc encircled by the loop: ∫ B ⋅ ds = μ₀ienc.

Solenoid

A long, tightly wound helical coil of wire. The magnetic field inside an ideal solenoid is uniform and parallel to its axis, with magnitude B = μ₀in (n = turns per unit length). The external field is approximately zero.

Toroid

A solenoid that has been curved into a hollow bracelet shape. The magnetic field inside a toroid at radius r is B = μ₀iN/(2πr) (N = total turns).

Magnetic Flux (ΦB)

The amount of magnetic field passing through an area, defined as ΦB = ∫ B ⋅ dA. The SI unit is the weber (Wb).

Faraday's Law of Induction

The magnitude of the emf (ε) induced in a conducting loop is equal to the rate at which the magnetic flux (ΦB) through the loop changes with time: ε = -dΦB/dt. For N turns, ε = -N dΦB/dt.

Lenz's Law

An induced current has a direction such that the magnetic field due to the current opposes the change in the magnetic flux that induces the current.

Induced Electric Field

A changing magnetic field produces an electric field (E), even in a vacuum. Related to induced emf by ∫ E ⋅ ds = -dΦB/dt.

Inductor

A device that can be used to produce a known magnetic field, characterized by its inductance L.

Inductance (L)

A measure of the magnetic flux linkage (NΦB) produced by an inductor per unit of current (i): L = NΦB/i. The SI unit is the henry (H).

Self-Induction

The process where an induced emf (εL) appears in any coil in which the current (i) is changing, opposing that change: εL = -L(di/dt).

RL Circuit (Current Rise)

A circuit with a resistor R and an inductor L connected to an emf ε. Current rises exponentially to ε/R: i = (ε/R)(1 - e^(-t/τL)), where τL = L/R is the inductive time constant.

RL Circuit (Current Decay)

When the emf is removed from an RL circuit, the current (initially i₀) decays exponentially: i = i₀e^(-t/τL).

Energy Stored in a Magnetic Field

The total energy (UB) stored by an inductor L carrying a current i: UB = (1/2)Li².

Magnetic Energy Density (uB)

The energy stored per unit volume of a magnetic field B, given by uB = B²/(2μ₀).

Mutual Induction (M)

The interaction between two coils where a changing current in one coil induces an emf in the other. It is defined as M = N₂Φ₂₁/i₁ (or N₁Φ₁₂/i₂), and the induced emfs are ε₁ = -M(di₂/dt) and ε₂ = -M(di₁/dt).