Charge and Current Review: Key Concepts

Vocabulary flashcards covering charge, charge density, current (scalar and vector), current densities (volumetric and surface), current through surfaces, charge conservation, continuity equation, capacitance, displacement current, and related concepts.

Charge

A fundamental property of matter that gives rise to electric forces; charge is conserved in ordinary processes, and can be moved but not created or destroyed.

Charge density (ρ)

Charge per unit volume at a point; the total charge in a region is ∫ρ dV.

Scalar current

The rate of charge flow through a defined surface treated as a scalar (magnitude only) without regard to direction.

Current (I)

The rate at which charge passes through a surface; a scalar quantity with sign depending on assumed direction; measured in amperes.

Volumetric current density (J_v)

Current per unit area flowing through a volume; a vector field with units of A/m^2; points in the direction of charge flow.

Surface current density (J_s)

Current per unit length flowing on a surface (negligible depth); a vector with units of A/m; describes current confined to a surface.

Current through a surface (δI)

The amount of charge per unit time crossing a small surface area; δI = J · δS.

Differential current relationship (dI = J · dS)

The infinitesimal current through a differential surface area dS given by the dot product of the current density and the differential area.

Direction of current density

The orientation of J that yields the maximum current through a surface; the direction of charge flow at that point.

Conservation of charge

Net outward current through a closed surface equals the negative rate of change of the enclosed charge: ∮ J · dS = -∂Q/∂t.

Charge inside a surface (Q enclosed)

Total charge contained within a given closed surface, used in applying charge conservation.

Continuity equation

Local form of charge conservation: ∇·J = -∂ρ/∂t; relates spatial change of current density to time change of charge density.

Capacitance (C)

Q = C V; stores charge on conductors; changing voltage across a capacitor induces current even though charges may not physically flow through the dielectric.

Displacement current

Effect of a changing electric field between capacitor plates that produces magnetic effects and ensures continuity in Ampère’s law, even without physical charge flow through the dielectric.

Conduction current vs displacement current

Conduction current is due to moving charges; displacement current arises from changing electric field; both contribute to the total current in a circuit.

Ben Franklin convention

Historical choice that positive current is in the direction of positive charge flow; electrons moving opposite create a negative actual current.

Convection current

Current due to bulk motion of charged particles (e.g., a moving charged cloud); quantified by J = ρ v.

Divergence of current density

∇·J describes the net outflow of current from a point; related to -∂ρ/∂t through the continuity equation.