Glossary
Area Charge Density (σ)
The amount of charge per unit area on a two-dimensional charge distribution, typically measured in Coulombs per square meter (C/m²).
Example:
A large metal plate with a uniform Area Charge Density (σ) of 10 nC/m² means every square meter of the plate holds 10 nanocoulombs of charge.
Conducting Sheets
Flat, electrically conductive surfaces where excess charge resides entirely on their surfaces, and the electric field inside the conductor is zero.
Example:
When two parallel Conducting Sheets are oppositely charged, a uniform electric field exists between them.
Electric Flux
A measure of the number of electric field lines passing through a given surface, representing the 'flow' of the electric field.
Example:
The Electric Flux through a closed surface enclosing no net charge is always zero.
Electric Potential (V)
A scalar quantity representing the electric potential energy per unit charge at a specific point in an electric field.
Example:
The Electric Potential (V) at a point near a positive charge is positive, indicating potential energy for a positive test charge.
Enclosed Charge (q_enc)
The total net electric charge contained within a chosen Gaussian surface, a key component in Gauss' Law calculations.
Example:
If a Gaussian surface surrounds both a +2Q and a -Q point charge, the Enclosed Charge (q_enc) is +Q.
Extended Charge Distributions
Physical objects where electric charge is spread out over a continuous region, rather than concentrated at a single point.
Example:
Calculating the electric field produced by a long, charged rod requires treating it as an Extended Charge Distribution rather than a simple point charge.
Gauss' Law
A fundamental law relating the electric flux through a closed surface to the net electric charge enclosed within that surface.
Example:
Gauss' Law is incredibly useful for quickly finding the electric field of highly symmetrical charge distributions, like spheres or cylinders.
Gaussian Surface
An imaginary closed surface chosen to exploit the symmetry of a charge distribution, simplifying the calculation of electric flux in Gauss' Law.
Example:
When applying Gauss' Law to a charged sphere, a concentric spherical Gaussian Surface is the ideal choice.
Insulating Sheet of Charge
A flat, non-conducting surface with electric charge uniformly distributed over its area.
Example:
The electric field produced by an infinite Insulating Sheet of Charge is uniform and perpendicular to the sheet.
Integration
A mathematical process used to sum up infinitesimal contributions (like dE or dV) from an extended charge distribution to find the total electric field or potential.
Example:
To find the total electric field from a charged disk, you must perform an Integration over all the differential charge elements.
Line of Charge
A specific extended charge distribution where charge is uniformly spread along a straight line segment or an infinitely long line.
Example:
The electric field near a long, straight power cable can be modeled as that of a Line of Charge.
Linear Charge Density (λ)
The amount of charge per unit length on a one-dimensional charge distribution, typically measured in Coulombs per meter (C/m).
Example:
A thin wire with a uniform Linear Charge Density (λ) of 5 nC/m means every meter of wire holds 5 nanocoulombs of charge.
Permittivity of Free Space (ε₀)
A fundamental physical constant representing the ability of a vacuum to permit electric field lines, appearing in Coulomb's Law and Gauss' Law.
Example:
The strength of the electric field in a vacuum is inversely proportional to the Permittivity of Free Space (ε₀).
Point Charges
Idealized charges that are considered to exist at a single point in space, simplifying electric field and potential calculations.
Example:
The electric field from a proton can often be approximated as that of a Point Charge when far away.
Potential Difference (ΔV)
The change in electric potential energy per unit charge between two points in an electric field, representing the work done per unit charge to move a charge between those points.
Example:
A battery creates a Potential Difference (ΔV) across its terminals, driving current through a circuit.
Ring of Charge
A specific extended charge distribution where charge is uniformly spread around a circular loop.
Example:
An electron orbiting a positively charged Ring of Charge would experience a restoring force towards the center.
Scalar
A physical quantity that has magnitude but no direction, such as electric potential, temperature, or mass.
Example:
Unlike electric field, which is a vector, electric potential is a Scalar, meaning you can simply add potentials from multiple sources.
Surface Area
The total area of the chosen Gaussian surface through which the electric field passes, used in Gauss' Law calculations.
Example:
For a cylindrical Gaussian surface, the relevant Surface Area for flux calculation includes both the curved side and the two end caps.
Symmetry
A property of a charge distribution that allows for simplification of electric field or potential calculations, especially when applying Gauss' Law.
Example:
Exploiting the spherical Symmetry of a charged sphere makes calculating its electric field with Gauss' Law much easier.
Uniformly Charged Sphere
A spherical object where electric charge is evenly distributed throughout its volume or on its surface.
Example:
The electric field inside a non-conducting Uniformly Charged Sphere increases linearly with distance from the center.
dE (differential electric field)
The infinitesimally small electric field contribution from a differential charge element (dq) at a specific point in space.
Example:
Each dE vector from a segment of a charged line points in a different direction, requiring vector integration to find the net field.
dq (differential charge)
An infinitesimally small piece of charge used when integrating over an extended charge distribution to find total electric fields or potentials.
Example:
To find the total electric field of a charged ring, we sum the contributions from each tiny dq element around the ring.