Glossary
Charge ($dq$)
A fundamental property of matter that causes it to experience a force in an electromagnetic field; $dq$ represents an infinitesimally small element of charge in continuous distributions.
Example:
When calculating the electric field from a charged rod, you break the rod into tiny segments, each carrying an infinitesimal amount of charge (dq).
Cylindrical Symmetry
A type of charge distribution where the charge is uniformly distributed along an infinite line or cylinder, leading to an electric field that points radially outward from the axis.
Example:
An infinitely long, uniformly charged wire demonstrates Cylindrical Symmetry, simplifying the calculation of its electric field using Gauss's Law.
Distance ($r$)
The scalar magnitude of the separation between an infinitesimal charge element ($dq$) and the specific point where the electric field is being measured.
Example:
For a point charge, the electric field strength decreases with the square of the distance (r) from the charge.
Electric Field Integration
A calculus-based method used to determine the total electric field produced by a continuous charge distribution by summing the vector contributions from infinitesimal charge elements.
Example:
Calculating the electric field along the axis of a charged ring requires Electric Field Integration to sum up the contributions from every tiny segment of the ring.
Electric field vector
A vector quantity representing the force per unit positive test charge experienced at a given point in space due to other charges.
Example:
When a positive test charge is placed near a positively charged sphere, the electric field vector at that point would point directly away from the sphere.
Finite wire or line charge
A charge distribution where charge is uniformly spread along a straight line segment of finite length, requiring integration to determine the electric field at various points.
Example:
To find the electric field at a point near a charged antenna, one might model it as a finite wire or line charge.
Infinitely long, uniformly charged wire or cylinder
A theoretical charge distribution used to model long, thin charged objects, where the electric field can be found using integration or Gauss's Law due to its cylindrical symmetry.
Example:
Determining the electric field around a power line can be approximated by treating it as an infinitely long, uniformly charged wire or cylinder.
Permittivity of free space
A fundamental physical constant ($\varepsilon_0$) that quantifies the ability of a vacuum to permit electric field lines, appearing in Coulomb's Law and Gauss's Law.
Example:
In calculating the electric field produced by a point charge, the constant is used to determine the field's strength.
Planar Symmetry
A type of charge distribution where the charge is uniformly distributed over an infinite plane, resulting in a uniform electric field perpendicular to the plane.
Example:
The electric field produced by a large, uniformly charged non-conducting sheet can be analyzed using Planar Symmetry, showing a constant field strength away from the sheet.
Semicircular arc
A charge distribution where charge is uniformly spread along a half-circle, requiring integration to find the electric field at its center or other points.
Example:
Calculating the electric field at the center of a charged semicircular arc involves integrating the contributions from each infinitesimal segment.
Spherical Symmetry
A type of charge distribution where the charge is uniformly distributed over a spherical surface or throughout a sphere, resulting in an electric field that points radially.
Example:
A uniformly charged conducting sphere exhibits Spherical Symmetry, meaning its electric field outside behaves like a point charge at its center.
Superposition Principle
States that the total electric field at any point due to a collection of charges is the vector sum of the electric fields produced by each individual charge.
Example:
To find the net electric field at the center of a square with charges at each corner, you would use the Superposition Principle to vectorially add the fields from each corner charge.
Thin ring of charge
A charge distribution where charge is uniformly spread along the circumference of a circular ring, often used to calculate the electric field along its central axis.
Example:
The electric field at the center of a charged particle accelerator's beam can be modeled as a thin ring of charge.
Unit vector ($\hat{r}$)
A vector with a magnitude of one that specifies the direction from the infinitesimal charge element ($dq$) to the point where the electric field is being calculated.
Example:
In the formula for electric field integration, the unit vector () ensures the direction of the field contribution from each dq is correctly accounted for.