Glossary
Ampère's Law
One of Maxwell's equations, it relates the magnetic field around a closed loop to the electric current passing through the loop and the rate of change of electric flux.
Example:
The magnetic field circling a current-carrying wire can be calculated using Ampère's Law, which is crucial for understanding electromagnets.
Area Vector (dA)
An infinitesimal vector element of a surface, whose magnitude is the area of the element and whose direction is normal (perpendicular) to the surface, pointing outwards for a closed surface.
Example:
When calculating electric flux, the area vector for a small patch of a spherical Gaussian surface points radially outward, parallel to the electric field.
Charge Enclosed (q_enc)
The net electric charge contained within a closed Gaussian surface. Only this charge contributes to the total electric flux through that specific surface.
Example:
If a Gaussian surface contains a +5 C charge and a -2 C charge, the charge enclosed by that surface is +3 C.
Cylindrical Symmetry
A charge distribution possesses cylindrical symmetry if its charge density depends only on the radial distance from a central axis. This allows for the use of a cylindrical Gaussian surface.
Example:
An infinitely long, uniformly charged rod has cylindrical symmetry, simplifying the electric field calculation with a cylindrical Gaussian surface.
Dot Product (E ⋅ dA)
A mathematical operation that takes two vectors and returns a scalar, representing the projection of one vector onto another. In flux calculations, it accounts for the angle between the electric field and the surface's area vector.
Example:
If the electric field is parallel to a surface, their dot product is zero, indicating no electric flux passes through that portion of the surface.
Electric Field (E)
A vector field that describes the force exerted on a positive test charge at any given point in space. It is generated by electric charges and changing magnetic fields.
Example:
The electric field lines around a positive point charge point radially outward, indicating the direction a positive test charge would accelerate.
Electric Flux (Φ_E)
A measure of the electric field passing through a given surface, representing the 'flow' of the electric field lines. It quantifies how much electric field 'pierces' a surface.
Example:
The electric flux through a closed spherical surface surrounding a point charge remains constant, regardless of the sphere's radius, as long as the enclosed charge doesn't change.
Faraday's Law
One of Maxwell's equations, it describes how a changing magnetic flux through a surface induces an electromotive force (and thus an electric field) around a closed loop.
Example:
A changing magnetic field from a moving magnet near a coil induces a current in the coil, a phenomenon explained by Faraday's Law.
Gauss's Law
A fundamental law in electromagnetism that relates the total electric flux through a closed surface to the total charge enclosed within that surface. It serves as a powerful shortcut for calculating electric fields, especially for symmetrical charge distributions.
Example:
Using Gauss's Law, one can quickly determine the electric field produced by an infinitely long charged wire without resorting to complex integration.
Gaussian Surface
An imaginary, closed three-dimensional surface strategically chosen to apply Gauss's Law for calculating electric fields. Its shape is typically selected to match the symmetry of the charge distribution.
Example:
To find the electric field of a uniformly charged sphere, a concentric spherical Gaussian surface is the ideal choice for simplifying calculations.
Linear Charge Density (λ)
The amount of electric charge per unit length, typically used for one-dimensional charge distributions like thin rods or wires.
Example:
A long, thin wire with 10 Coulombs of charge spread uniformly over 5 meters has a linear charge density of 2 C/m.
Maxwell's Equations
A set of four fundamental equations that describe how electric and magnetic fields are generated and altered by each other and by charges and currents. Gauss's Law is one of these foundational equations.
Example:
The propagation of light as an electromagnetic wave is a direct consequence of Maxwell's Equations, unifying electricity and magnetism.
Permittivity of Free Space (ε₀)
A fundamental physical constant that represents the ability of a vacuum to permit electric field lines. It is a proportionality constant in Coulomb's Law and Gauss's Law.
Example:
The strength of the electric field generated by a point charge in a vacuum is inversely proportional to the permittivity of free space.
Planar Symmetry
A charge distribution possesses planar symmetry if its charge density depends only on the distance from a central plane. This allows for the use of a pillbox-shaped Gaussian surface.
Example:
An infinite, uniformly charged sheet demonstrates planar symmetry, where the electric field lines are perpendicular to the sheet.
Spherical Symmetry
A charge distribution possesses spherical symmetry if its charge density depends only on the distance from a central point. This allows for the use of a spherical Gaussian surface.
Example:
A uniformly charged solid sphere exhibits spherical symmetry, making electric field calculations straightforward using Gauss's Law.
Surface Charge Density (σ)
The amount of electric charge per unit area, typically used for two-dimensional charge distributions like charged sheets or the surfaces of conductors.
Example:
A charged metal plate with 5 Coulombs spread over 2 square meters has a surface charge density of 2.5 C/m².
Volume Charge Density (ρ)
The amount of electric charge per unit volume, typically used for three-dimensional charge distributions like charged spheres or cylinders.
Example:
A uniformly charged non-conducting sphere with 10 Coulombs of charge in a volume of 1 m³ has a volume charge density of 10 C/m³.