Gauss's Law for electricity is one of the fundamental equations in electromagnetism, formulated by Carl Friedrich Gauss. It relates the electric flux through a closed surface to the total charge enclosed within that surface. In mathematical terms, Gauss's Law for electricity is expressed as:
∮ E ⋅ dA = ε₀ * Q_enclosed
Where:
∮ represents the surface integral over a closed surface.
E is the electric field vector.
dA is an infinitesimal vector representing a differential area element on the closed surface.
ε₀ (epsilon naught) is the vacuum permittivity or electric constant, which is a fundamental constant of nature.
Q_enclosed is the total electric charge enclosed by the closed surface.
In simpler terms, the equation states that the total electric flux passing through a closed surface is proportional to the total charge enclosed within that surface. This is a powerful tool for calculating electric fields due to symmetric charge distributions and is often used to find electric fields in situations with high symmetry, such as charged spheres, cylinders, or planes.