AP Physics C: E&M flashcards

33 cards. Read the term and the definition here. The deck at the top of this page is optional.

Coulomb's law

The electrostatic force between two point charges is F = kq₁q₂/r², directed along the line joining them; repulsive for like signs, attractive for opposite signs.

Electric field definition

The electric field at a point is the force per unit positive test charge placed there: E = F/q, a vector pointing the way a positive charge would be pushed.

Gauss's law

The net electric flux through any closed surface equals the enclosed charge divided by ε₀: ∮E·dA = Q_enc/ε₀. Charge outside contributes zero net flux.

Field inside a conductor

In electrostatic equilibrium the electric field everywhere inside a conductor is zero, so excess charge resides entirely on the outer surface.

Field of infinite sheet

An infinite sheet with surface charge density σ produces a uniform field E = σ/(2ε₀) normal to the sheet, independent of distance from it.

Electric potential difference

The potential difference V_b − V_a equals the negative line integral of the electric field from a to b: ΔV = −∫E·ds.

Point-charge potential

With V = 0 at infinity, the potential at distance r from a point charge q is V = kq/r, a scalar that can be positive or negative.

Field from potential

The electric field is the negative gradient of the potential: E = −dV/dx in one dimension, or E = −∇V generally; field points toward lower potential.

Equipotential surfaces

Surfaces on which the electric potential is constant. They are everywhere perpendicular to electric field lines, and no work is done moving charge along them.

Potential energy of two charges

The electric potential energy of two point charges is U = kq₁q₂/r, equal to the work an external agent does assembling them from infinite separation.

Capacitance definition

Capacitance is the ratio of stored charge to potential difference: C = Q/V, determined by geometry and dielectric, measured in farads.

Parallel-plate capacitance

For two plates of area A separated by distance d, C = ε₀A/d; filling the gap with a dielectric of constant κ multiplies C by κ.

Energy in a capacitor

A charged capacitor stores energy U = ½QV = ½CV² = Q²/(2C); in a dielectric the energy density is u = ½κε₀E².

Capacitors in series

Capacitors in series carry the same charge and combine reciprocally: 1/C_eq = 1/C₁ + 1/C₂ + …, giving an equivalent capacitance smaller than any single one.

Capacitors in parallel

Capacitors in parallel share the same voltage and add directly: C_eq = C₁ + C₂ + …, giving an equivalent capacitance larger than any single one.

Ohm's law and resistance

For an ohmic resistor V = IR; the resistance of a uniform wire of resistivity ρ, length L, and cross-sectional area A is R = ρL/A.

Kirchhoff's junction rule

At any circuit junction, the total current entering equals the total current leaving, a consequence of conservation of electric charge.

Kirchhoff's loop rule

Around any closed circuit loop, the algebraic sum of potential differences is zero, a consequence of conservation of energy.

Resistors in parallel

Resistors in parallel share the same voltage and combine reciprocally: 1/R_eq = 1/R₁ + 1/R₂ + …, giving an equivalent resistance smaller than any single one.

RC time constant

For an RC circuit the time constant is τ = RC; after one τ a charging capacitor reaches about 63% of its final charge.

Electric power in resistor

The rate at which a resistor dissipates energy is P = IV = I²R = V²/R, all equivalent for an ohmic resistor.

Magnetic force on charge

A charge moving in a magnetic field feels F = qv×B, magnitude qvB sinθ; the force is perpendicular to v and does no work.

Circular motion radius in B

A charge moving perpendicular to a uniform magnetic field follows a circle of radius r = mv/(|q|B), with period T = 2πm/(|q|B) independent of speed.

Field of a long wire

A long straight wire carrying current I produces B = μ₀I/(2πr) at distance r, with circular field lines given by the right-hand rule.

Solenoid magnetic field

Inside a long solenoid with n turns per unit length carrying current I, the field is uniform: B = μ₀nI, directed along the axis.

Ampère's law

The line integral of B around a closed loop equals μ₀ times the enclosed current: ∮B·ds = μ₀I_enc; useful with high symmetry.

Magnetic dipole moment

A current loop of area A carrying current I has magnetic moment μ = IA normal to the loop; in a field, torque τ = μ×B and U = −μ·B.

Faraday's law of induction

The induced emf around a loop equals the negative rate of change of magnetic flux through it: emf = −dΦ_B/dt, or −N dΦ_B/dt for N turns.

Lenz's law

The induced current flows in the direction that opposes the change in magnetic flux that produced it, ensuring energy conservation in induction.

Motional emf

A conducting rod of length L moving at speed v perpendicular to a uniform magnetic field B develops an emf of magnitude BLv across its ends.

Magnetic flux

Magnetic flux through a surface is Φ_B = ∫B·dA, or BA cosθ for a flat loop in a uniform field; measured in webers.

Inductor energy and emf

An inductor opposes current change with emf = −L dI/dt and stores energy U = ½LI²; the henry is the unit of inductance.

LR circuit time constant

In an LR circuit the current approaches its final value ε/R with time constant τ = L/R, reaching about 63% of the final value after one τ.