6.1 Electric current and current density

Electric current is the flow of charge through a conductor, measured in amperes. It's a fundamental concept in electromagnetism, describing how charges move in response to electric fields.

Current density and drift velocity dive deeper into the mechanics of charge flow. These concepts help us understand how current distributes in conductors and how individual charge carriers behave under electric fields.

Electric Current Fundamentals

Defining Electric Current

• Electric current is the rate of flow of electric charge through a conducting material
• Measured in amperes (A), which is the flow of one coulomb of charge per second
• Can be expressed mathematically as $I = \frac{dq}{dt}$, where $I$ is current, $q$ is charge, and $t$ is time
• Conventional current assumes positive charges flow from positive to negative terminals, although in most conductors, electrons (negative charges) are the actual charge carriers

Types of Charge Carriers

• Charge carriers are particles that carry electric charge and facilitate current flow
• In metals, charge carriers are typically free electrons that move through the material
• In semiconductors, charge carriers can be electrons or holes (positive charge carriers)
• In electrolytes (solutions or molten salts), charge carriers are ions (positive cations and negative anions) that move toward oppositely charged electrodes
• In gases and plasmas, charge carriers can be electrons and ions

Current Density and Drift Velocity

Current Density

• Current density ($\vec{J}$) is a vector quantity that describes the flow of electric current per unit cross-sectional area
• Measured in amperes per square meter (A/m²)
• Mathematically expressed as $\vec{J} = \frac{I}{A}$, where $I$ is current and $A$ is the cross-sectional area perpendicular to the flow
• Current density is useful for analyzing the distribution of current in a conductor (higher current density in thinner wires, lower in thicker wires)
• In non-uniform conductors, current density can vary across the cross-section

Drift Velocity

• Drift velocity ($v_d$) is the average velocity of charge carriers in a conductor due to an applied electric field
• Typically much lower than the random thermal motion of charge carriers (on the order of mm/s for electrons in metals)
• Related to current density by $\vec{J} = nq\vec{v_d}$, where $n$ is the number of charge carriers per unit volume and $q$ is the charge of each carrier
• Depends on factors such as the applied electric field, the material's resistivity, and the charge carrier mobility
• Higher drift velocities generally result in higher current densities

Continuity Equation

• The continuity equation relates the change in charge density over time to the divergence of the current density
• Mathematically expressed as $\frac{\partial \rho}{\partial t} + \nabla \cdot \vec{J} = 0$, where $\rho$ is the charge density and $\nabla \cdot \vec{J}$ is the divergence of the current density
• Represents the conservation of electric charge in a system
• In steady-state conditions (constant current), the divergence of the current density is zero, meaning the current flowing into a region equals the current flowing out
• The continuity equation is essential for analyzing time-dependent current flows and charge distributions in circuits and devices (capacitors, diodes)