AP Physics C: Electricity and Magnetism Vocabulary

Ammeter

An instrument used to measure the electric current flowing through a circuit, connected in series with the component being measured.

Example: "The student connected the          in series with the resistor to determine how much current was flowing through the circuit."

Ampere

The SI unit of electric current, defined as one coulomb of charge passing a point per second (1 A = 1 C/s).

Similar definitions: amp

Example: "A current of two          means that two coulombs of charge flow past a given point every second."

Ampere's law

A law stating that the line integral of the magnetic field around a closed loop equals μ₀ times the net electric current passing through the loop: ∮B·dl = μ₀I_enc. The generalized form includes the displacement current term.

Example: "Using         , the student calculated the magnetic field inside a long solenoid by choosing a rectangular Amperian loop."

Amperian loop

An imaginary closed path chosen to exploit symmetry when applying Ampere's law to calculate the magnetic field, analogous to a Gaussian surface for Gauss's law.

Example: "The student drew a rectangular          with one side inside the solenoid and one side outside to find the magnetic field."

Area vector

A vector whose magnitude equals the area of a surface and whose direction is perpendicular (normal) to that surface.

Example: "To compute electric flux, the student took the dot product of the electric field with the          of each face of the cube."

Biot-Savart law

An equation that gives the magnetic field at a point in space produced by a small segment of current-carrying wire, used to calculate fields from arbitrary current distributions.

Example: "The student used the          to derive the magnetic field at the center of a circular current loop by integrating contributions from each infinitesimal wire segment."

Capacitance

The amount of electric charge a device can store per unit voltage applied across it, measured in farads (F).

Example: "Increasing the area of the plates or decreasing the distance between them will increase the          of a parallel-plate capacitor."

Capacitor

A device consisting of two conductors separated by an insulator that stores electrical energy in the electric field between them.

Example: "The          in the camera flash circuit stores charge and then releases it rapidly to produce a bright burst of light."

Capacitors in series and parallel

Rules for combining capacitors: in series, 1/C_eq = 1/C₁ + 1/C₂ + ... (voltage divides, charge is the same); in parallel, C_eq = C₁ + C₂ + ... (charge divides, voltage is the same).

Example: "Using the rules for         , the student found that two 10 μF capacitors in series have an equivalent capacitance of 5 μF."

Charging by conduction

The process of transferring electric charge from one object to another through direct physical contact.

Example: "When the charged rod touched the metal sphere,          occurred and the sphere acquired the same sign of charge as the rod."

Charging by induction

A process by which an electrically charged object brought near a neutral conductor creates a charge separation in that conductor without direct contact.

Example: "By bringing a negative rod near the sphere and then grounding the sphere, the student used          to give the sphere a net positive charge."

Circuit

A complete closed path through which electric current can flow from a source, through components, and back to the source.

Similar definitions: electric circuit, closed circuit

Example: "The lightbulb only illuminated when the switch was closed, completing the          and allowing current to flow."

Conductor

A material that allows electric charges to move freely through it, such as metals, because it has a large number of free electrons.

Example: "Copper is an excellent          because its outer electrons are loosely bound and can easily drift under an applied electric field."

Conservation of charge

A fundamental law stating that the net electric charge of an isolated system remains constant; charge can be transferred but cannot be created or destroyed.

Example: "When a glass rod is rubbed with silk, electrons transfer to the silk, but the          principle ensures the total charge of the system stays zero."

Continuous charge distribution

A source charge composed of so many elementary charges that it is treated as a continuous distribution characterized by a charge density rather than as discrete point charges.

Example: "To find the electric field of a charged disk, the student modeled it as a          and integrated over infinitesimal ring elements."

Conventional current

The direction of current flow defined as the direction positive charges would move in a circuit, from the positive terminal to the negative terminal of a source.

Example: "Although electrons actually flow from negative to positive,          is defined as flowing in the opposite direction for historical reasons."

Coulomb

The SI unit of electric charge, equivalent to the charge of approximately 6.24 × 10¹⁸ electrons or protons.

Example: "One          is a very large amount of charge; typical static electricity experiments involve charges on the order of microcoulombs."

Coulomb's constant

The proportionality constant k = 1/(4πε₀) ≈ 8.99 × 10⁹ N·m²/C² appearing in Coulomb's law and expressions for electric potential and field due to point charges.

Example: "The electric field at a distance r from a point charge Q is E =          × Q/r²."

Coulomb's law

The mathematical equation stating that the electrostatic force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Example: "Using         , the student calculated that doubling the distance between two charges reduces the force to one-quarter of its original value."

Current density

The amount of electric current flowing per unit cross-sectional area of a conductor, expressed as a vector in the direction of current flow (J = I/A).

Example: "Even though the same current flows through both wires, the thinner wire has a higher          because the charge carriers are squeezed into a smaller area."

Diamagnetic material

A material whose magnetic dipoles align opposite to an applied magnetic field, producing a very weak repulsive effect that disappears when the field is removed.

Example: "Bismuth is a          and is slightly repelled when placed near a strong magnet."

Dielectric

An insulating material placed between the plates of a capacitor that increases capacitance by reducing the electric field through polarization of its molecules.

Example: "Inserting a          between the capacitor plates increased the capacitance by a factor equal to the material's dielectric constant."

Dielectric constant

A dimensionless factor (κ) by which the capacitance of a capacitor increases when a dielectric material is inserted between its plates.

Similar definitions: relative permittivity

Example: "Water has a very high          of about 80, which is why it is such an effective solvent for ionic compounds."

Dipole

A system of two equal and opposite charges separated by a fixed distance, producing a characteristic electric field pattern.

Similar definitions: electric dipole

Example: "A water molecule behaves as a permanent          because the oxygen end carries a partial negative charge and the hydrogen end carries a partial positive charge."

Dipole moment

A vector quantity (p = qd) that characterizes an electric dipole, pointing from the negative to the positive charge with magnitude equal to the product of charge magnitude and separation distance.

Similar definitions: electric dipole moment

Example: "The torque on the          in a uniform electric field is given by τ = p × E, which tends to align the dipole with the field."

Displacement current

A term in Maxwell's equations proportional to the rate of change of the electric flux, which acts as a source of magnetic field just like a real current.

Example: "Between the plates of a charging capacitor, there is no actual flow of charge, but the changing electric field creates a          that produces a magnetic field."

Drift velocity

The average velocity at which charge carriers move through a conductor under the influence of an applied electric field, typically very slow compared to the speed of the signal.

Example: "Although the          of electrons in a copper wire is only about 0.1 mm/s, the electrical signal propagates at nearly the speed of light."

Electric charge

A fundamental physical property of matter that causes it to experience a force when placed near other electrically charged matter, existing in two types: positive and negative.

Example: "         is quantized, meaning it always occurs in integer multiples of the elementary charge e ≈ 1.6 × 10⁻¹⁹ C."

Electric current

The rate at which electric charge flows past a point in a circuit, measured in amperes (I = dQ/dt).

Example: "The          through the resistor was measured to be 2 A, meaning 2 coulombs of charge passed through it every second."

Electric field

A vector field surrounding electric charges that exerts a force on other charges placed within it, defined as the force per unit positive test charge (E = F/q).

Example: "The          points radially outward from a positive point charge and its magnitude decreases with the square of the distance."

Electric field lines

Continuous curves drawn in space that indicate the direction and relative strength of the electric field; they originate on positive charges and terminate on negative charges.

Example: "The density of          is greater near the charge, indicating a stronger field in that region."

Electric flux

The dot product of the electric field and the area vector through which it passes, representing the number of field lines penetrating a surface (Φ_E = ∫E·dA).

Example: "The          through a closed surface surrounding a positive charge is positive and proportional to the enclosed charge."

Electric potential

The electric potential energy per unit charge at a point in an electric field, measured in volts (V = U/q).

Similar definitions: potential

Example: "The          at a distance r from a point charge Q is kQ/r, and it decreases as you move further from the charge."

Electric potential difference

The change in potential energy per unit charge as a charge moves between two points in an electric field, equal to the work done per unit charge.

Similar definitions: voltage, potential difference

Example: "A 9-volt battery maintains an          of 9 V between its terminals, driving current through any connected circuit."

Electric potential due to a point charge

The scalar potential at a distance r from a point charge Q, given by V = kQ/r, measured relative to zero potential at infinity.

Example: "The          was positive near a proton and negative near an electron, both decreasing in magnitude with distance."

Electric potential energy

The energy stored in a system of charged objects due to their positions relative to each other in an electric field.

Example: "The          of two like charges increases as they are pushed closer together, since work must be done against the repulsive force."

Electric power

The rate at which electrical energy is transferred or converted in a circuit, equal to the product of voltage and current (P = IV).

Example: "The          dissipated by the 100-ohm resistor carrying 0.5 A of current was P = I²R = 25 watts."

Electromagnetic induction

The process by which a changing magnetic flux through a circuit induces an electromotive force (EMF) in that circuit, as described by Faraday's law.

Example: "         is the operating principle behind electric generators, transformers, and induction cooktops."

Electromagnetic wave

A transverse wave consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation, traveling at c = 1/√(μ₀ε₀) in vacuum.

Example: "Maxwell showed that          travel at the speed of light, confirming that light itself is an electromagnetic phenomenon."

Electromotive force (EMF)

The energy produced per unit charge by a source such as a battery or generator that drives current through a circuit, measured in volts.

Example: "Despite its name,          is not actually a force but rather a voltage that represents the energy per coulomb supplied by the source."

Electrostatic equilibrium

The condition in which all charges in a conductor are at rest, resulting in zero electric field inside the conductor and any excess charge residing on its surface.

Example: "A hollow metal sphere in          has all its excess charge on the outer surface and zero electric field in its interior."

Electrostatic force

The attractive or repulsive force between two stationary charged objects, governed by Coulomb's law.

Similar definitions: Coulomb force

Example: "The          between a proton and an electron in a hydrogen atom is about 8.2 × 10⁻⁸ N, directed radially inward."

Energy density

The energy stored per unit volume in an electric or magnetic field, given by u_E = ½ε₀E² for electric fields and u_B = B²/(2μ₀) for magnetic fields.

Example: "The          of the electric field between the capacitor plates was calculated using ½ε₀E²."

Energy stored in a capacitor

The potential energy stored in the electric field of a charged capacitor, given by U = ½CV² = ½QV = Q²/(2C).

Example: "The          was released as a bright flash when the capacitor was discharged through the flashtube."

Energy stored in an inductor

The energy stored in the magnetic field of a current-carrying inductor, given by U = ½LI².

Example: "The          reached its maximum value when the current through the coil was at its peak."

Equipotential surface

A surface in space on which every point has the same electric potential, meaning no work is done moving a charge along it.

Similar definitions: equipotential line

Example: "         around a point charge are concentric spheres, always perpendicular to the electric field lines."

Equivalent resistance

The single resistance value that could replace a combination of resistors and draw the same current from the same voltage source.

Example: "The          of three 6 Ω resistors in parallel is 2 Ω, since 1/R_eq = 1/6 + 1/6 + 1/6."

Farad

The SI unit of capacitance, equal to one coulomb per volt (1 F = 1 C/V); typical capacitors have capacitances measured in microfarads or picofarads.

Example: "One          is an extremely large capacitance; most practical capacitors are rated in microfarads (μF) or nanofarads (nF)."

Faraday's law

A law stating that the induced EMF in a closed loop equals the negative rate of change of magnetic flux through the loop (ε = −dΦ_B/dt).

Example: "According to         , moving a magnet faster toward a coil induces a larger voltage because the flux changes more rapidly."

Ferromagnetic material

A material containing magnetic domains that strongly align with an applied magnetic field and retain their magnetization after the field is removed.

Example: "Iron, cobalt, and nickel are          that can be permanently magnetized and are used to make strong permanent magnets."

Gauss's law

A law stating that the total electric flux through any closed surface is proportional to the net electric charge enclosed within that surface (Φ_E = Q_enc/ε₀).

Example: "Using         , the student proved that the electric field inside a uniformly charged hollow sphere is zero."

Gauss's law for magnetism

A law stating that the net magnetic flux through any closed surface is always zero, implying that magnetic monopoles do not exist.

Example: "         tells us that every magnetic field line that enters a closed surface must also exit it, because isolated north or south poles cannot exist."

Gaussian surface

An imaginary closed surface used in Gauss's law to relate the electric flux through the surface to the charge enclosed within it.

Example: "To find the electric field of a uniformly charged sphere, the student chose a spherical          concentric with the charge distribution."

Grounding

The process of connecting a conductor to the Earth to neutralize excess charge or to ensure it remains at zero potential.

Example: "         the metal sphere after induction charging allowed electrons to flow to Earth, leaving the sphere with a net positive charge."

Hall effect

The creation of a voltage difference across an electrical conductor carrying current, caused by a magnetic field perpendicular to the current direction.

Example: "The          is used in sensors to measure magnetic field strength and to determine the sign and density of charge carriers in a material."

Henry

The SI unit of inductance, equal to one volt-second per ampere (1 H = 1 V·s/A).

Example: "The solenoid had a self-inductance of 0.5         , meaning a current change of 1 A/s would induce an EMF of 0.5 V."

Induced electric field

A non-conservative electric field created by a changing magnetic flux, as described by Faraday's law, whose field lines form closed loops.

Example: "Unlike the electric field from static charges, the          produced by a changing magnetic flux has field lines that form closed loops and is non-conservative."

Induced EMF

A voltage generated in a conductor or coil due to a changing magnetic flux through it, as described by Faraday's law.

Example: "The          in the coil increased when the magnet was moved faster, because the rate of change of magnetic flux was greater."

Inductance

A property of an electrical component (such as a coil) that quantifies its ability to oppose changes in current by inducing an EMF proportional to the rate of current change (ε = −L dI/dt), measured in henries.

Similar definitions: self-inductance

Example: "The          of the solenoid determined how large an EMF was induced when the current changed rapidly."

Inductive time constant

The time τ = L/R that characterizes how quickly current builds up or decays in an RL circuit, equal to the inductance divided by the resistance.

Example: "After one         , the current in the RL circuit reaches approximately 63% of its final steady-state value."

Inductor

A circuit component, typically a coil of wire, designed to store energy in its magnetic field and oppose changes in current through self-inductance.

Example: "The          in the circuit resisted the sudden change in current when the switch was opened, producing a brief voltage spike."

Insulator

A material that strongly resists the flow of electric current because its electrons are tightly bound to their atoms.

Example: "Glass, rubber, and plastic are common          used to coat wires and prevent unwanted current flow."

Internal resistance

The inherent resistance within a voltage source, such as a battery, that causes the terminal voltage to be less than the EMF when current flows.

Example: "The battery's          caused the terminal voltage to drop from 12 V to 11.5 V when a large current was drawn."

Junction rule

Kirchhoff's rule stating that the sum of all currents entering a junction must equal the sum of all currents leaving that junction, based on conservation of charge.

Similar definitions: Kirchhoff's current law, KCL

Example: "Applying the          at the node where three wires meet, the student wrote I₁ = I₂ + I₃."

Kirchhoff's rules

A set of two rules—the junction rule (conservation of charge) and the loop rule (conservation of energy)—used to analyze complex electric circuits.

Example: "The student applied          to write a system of equations for the multi-loop circuit and solved for all unknown currents."

LC circuit

A circuit containing an inductor and capacitor that oscillates as energy transfers back and forth between the electric field of the capacitor and the magnetic field of the inductor.

Example: "The charge on the capacitor in the          oscillated sinusoidally at the natural frequency ω = 1/√(LC)."

Lenz's law

A law stating that the direction of an induced current is always such that it opposes the change in magnetic flux that produced it.

Example: "According to         , when a magnet is pushed into a coil, the induced current flows in the direction that creates a magnetic field opposing the magnet's approach."

Linear charge density

The amount of electric charge per unit length along a one-dimensional charge distribution, measured in coulombs per meter (C/m).

Similar definitions: λ (lambda)

Example: "The          of the uniformly charged rod was 5 μC/m, so a 2-meter segment carried a total charge of 10 μC."

Loop rule

Kirchhoff's rule stating that the algebraic sum of all potential differences around any closed loop in a circuit must equal zero, based on conservation of energy.

Similar definitions: Kirchhoff's voltage law, KVL

Example: "Applying the         , the student summed the EMF of the battery and the voltage drops across the resistors and set the total equal to zero."

Lorentz force

The total electromagnetic force on a charged particle, equal to the sum of the electric force and the magnetic force: F = q(E + v × B).

Example: "The          on the proton moving through both electric and magnetic fields determined its curved trajectory in the velocity selector."

Magnetic dipole

A current loop or pair of magnetic poles that produces a magnetic field pattern similar to that of a small bar magnet.

Example: "An electron orbiting the nucleus acts as a tiny         , producing a magnetic field that contributes to the atom's overall magnetic properties."

Magnetic dipole moment

A vector quantity (μ = NIA) that characterizes the strength and orientation of a magnetic dipole, equal to the product of current, area, and number of loops.

Example: "The          of the 100-turn coil carrying 2 A with area 0.01 m² was 2 A·m²."

Magnetic domain

A region within a ferromagnetic material where the magnetic dipoles of atoms are aligned in the same direction.

Example: "When an external field is applied, the          aligned with the field grow at the expense of those aligned against it, magnetizing the material."

Magnetic field

A vector field produced by moving charges or changing electric fields that exerts a force on other moving charges and magnetic materials.

Example: "A current-carrying wire produces a          that forms concentric circles around the wire, as predicted by the right-hand rule."

Magnetic field lines

Continuous curves that indicate the direction and relative strength of the magnetic field; they always form closed loops, exiting from north poles and entering south poles.

Example: "Unlike electric field lines,          never begin or end at a point—they always form complete closed loops."

Magnetic flux

The measure of the total magnetic field passing through a given area, calculated as the integral of B·dA over the surface, measured in webers (Wb).

Example: "The          through the loop decreased as it was rotated away from being perpendicular to the field, inducing an EMF."

Magnetic force

The force exerted on a moving charged particle by a magnetic field, given by F = qv × B, always perpendicular to both the velocity and the field.

Example: "The          on the proton caused it to travel in a circular path because the force was always perpendicular to its velocity."

Magnetic force on a current-carrying wire

The force exerted on a straight current-carrying conductor in a magnetic field, given by F = IL × B, where I is the current, L is the length vector along the wire, and B is the magnetic field.

Example: "The          was directed upward when the current flowed east through a region where the magnetic field pointed north."

Maxwell's equations

A set of four fundamental equations that form a complete description of classical electromagnetism: Gauss's law, Gauss's law for magnetism, Faraday's law, and the Ampère-Maxwell law.

Example: "         unified electricity and magnetism and predicted the existence of electromagnetic waves traveling at the speed of light."

Motional EMF

The voltage induced when a conducting rod or wire moves through a magnetic field, given by ε = BLv for a straight conductor moving perpendicular to the field.

Example: "The          generated by the metal rod sliding along the rails was calculated as the product of the field strength, rod length, and velocity."

Mutual inductance

A property describing how effectively a changing current in one coil induces an EMF in a nearby coil, depending on the geometry and proximity of the coils.

Example: "The transformer's operation relies on          between its primary and secondary coils to transfer energy at a different voltage."

Ohm

The SI unit of electrical resistance, defined as the resistance that produces a one-ampere current when a one-volt potential difference is applied (1 Ω = 1 V/A).

Example: "The resistor was rated at 470         , meaning a 4.7 V potential difference would drive a current of 10 mA through it."

Ohm's law

An empirical relation stating that the current through a conductor is directly proportional to the voltage across it and inversely proportional to its resistance (V = IR).

Example: "Using         , the student determined that doubling the voltage across the resistor would double the current flowing through it."

Parallel circuit

A circuit configuration in which components are connected across the same two nodes, providing multiple paths for current flow and maintaining the same voltage across each component.

Example: "In a         , each resistor experiences the full battery voltage, and the total current is the sum of the currents through each branch."

Parallel-plate capacitor

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

Example: "The electric field between the plates of a          is uniform and equals σ/ε₀, where σ is the surface charge density."

Paramagnetic material

A material whose atomic magnetic dipoles partially align with an applied magnetic field, producing a weak attractive effect that disappears when the field is removed.

Example: "Aluminum and platinum are          that are weakly attracted to strong magnets but do not retain any magnetization."

Permeability of free space

The constant μ₀ = 4π × 10⁻⁷ T·m/A that describes the ability of a vacuum to support a magnetic field, appearing in Ampère's law and the Biot-Savart law.

Example: "The          appears in the formula for the magnetic field inside a solenoid: B = μ₀nI."

Permittivity of free space

The constant ε₀ ≈ 8.85 × 10⁻¹² C²/(N·m²) that describes the strength of the electric force in a vacuum, appearing in Coulomb's law and Gauss's law.

Example: "The          relates the electric flux through a closed surface to the charge enclosed, via Gauss's law."

Point charge

An idealized model of a charged particle in which all the charge is concentrated at a single point in space, used to simplify calculations.

Example: "Coulomb's law gives the exact force between two         , and it is a good approximation when charged objects are far apart compared to their size."

Polarization

The slight shifting of positive and negative charges to opposite sides of a neutral object or dielectric molecule in response to an external electric field.

Example: "         of the dielectric material reduced the net electric field between the capacitor plates and increased the capacitance."

Potential drop

The decrease in electric potential energy as current flows through a resistor or other circuit component, equal to IR for a resistor.

Similar definitions: voltage drop

Example: "The          across the 10 Ω resistor carrying 3 A of current was 30 V."

Principle of superposition

The principle stating that the net electric field or force at any point due to multiple charges is the vector sum of the fields or forces produced by each charge individually.

Example: "Using the         , the student found the total electric field at point P by adding the field vectors from each of the four point charges."

RC circuit

A circuit containing a resistor and capacitor in which the voltage and current change exponentially during charging and discharging, with time constant τ = RC.

Example: "In the         , the capacitor charged to 63% of the battery voltage after one time constant τ = RC."

Relationship between E and V

The electric field is the negative gradient of the electric potential: E = −dV/dr (in one dimension) or E = −∇V (in three dimensions). Equivalently, the potential difference is the negative line integral of the electric field.

Example: "Using the         , the student determined the electric field from the slope of the voltage-versus-position graph."

Resistance

A measure of the opposition to current flow in a conductor, equal to the ratio of voltage to current for ohmic materials (R = V/I), measured in ohms.

Example: "The          of a wire increases with length and decreases with cross-sectional area, according to R = ρL/A."

Resistivity

An intrinsic property of a material that quantifies how strongly it opposes electric current flow, independent of the object's shape or size, measured in ohm-meters (Ω·m).

Example: "Copper has a very low          of about 1.7 × 10⁻⁸ Ω·m, which is why it is widely used in electrical wiring."

Resistor

A circuit component designed to provide a specific amount of resistance to current flow, converting electrical energy into thermal energy.

Example: "The 1 kΩ          was used as a current limiter to protect the LED from excessive current."

Resistors in series and parallel

Rules for combining resistors: in series, R_eq = R₁ + R₂ + ... (current is the same, voltage divides); in parallel, 1/R_eq = 1/R₁ + 1/R₂ + ... (voltage is the same, current divides).

Example: "Using the rules for         , the student calculated that two 100 Ω resistors in parallel have an equivalent resistance of 50 Ω."

Right-hand rule

A mnemonic for determining the direction of magnetic force, field, or angular quantities: point fingers in the direction of the first vector, curl toward the second, and the thumb gives the cross product direction.

Example: "Using the         , the student determined that the magnetic force on a positive charge moving east in a field pointing north would be directed upward."

RL circuit

A circuit containing a resistor and inductor in which current grows or decays exponentially with time constant τ = L/R when a voltage is applied or removed.

Example: "When the switch was closed, the current in the          rose exponentially toward its maximum value of ε/R with time constant L/R."