Calculated using Coulomb’s Law for a single point or many point charges.
Principle of Superposition is used for multiple charges.
Gauss’s Law
A different, more general and fundamental method for calculating electric fields.
Provides the connection between the number of field lines and the charge that produces them.
The flux through a surface, regardless of its shape, is determined solely by the amount of charge inside, divided by a constant ε.
Electric Field Lines
Produced by a charged object.
Imaginary closed surfaces (bubbles) are drawn around the object.
Field lines cross both bubbles and continue throughout space.
Field is weaker at the surface of the larger bubble due to greater surface area.
Number of field lines crossing is the same for both bubbles.
Flux
Proxy for the number of field lines.
Depends on the electric field strength and the area.
Defined as an integral over a surface of the electric field.
Only the field components that are normal to the surface are considered.
For a flat surface in a uniform field, the integral simplifies to the magnitude of the electric field times the area times the cosine of the angle between the normal to the surface and the electric field.
The flux is maximum when the surface is oriented face-on to the field and zero when the surface is side-on to the field.
Applying Gauss’s Law
The flux (magnitude of the electric field times the area of the surface) is equal to the charge inside divided by a constant ε.
Substituting the area of the sphere (4πr2) gives the familiar form of Coulomb’s Law, showing that the electric field falls off as r2.
Gauss’s Law is more general and fundamental than Coulomb’s Law.
Even in cases where Coulomb’s Law fails (e.g., for charges that are moving around dynamically), Gauss’s Law still holds.
Gauss’s Law is one of the fundamental laws of electromagnetism.