Equations · Physics
Gauss's law
Electric field lines start and end on charges: the divergence of the field equals the charge density over ε₀.
∇ · E = ρ / ε₀
Aethel says
the divergence of E equals rho over epsilon naught
What it says
Where there is positive charge, the electric field spreads outwards; where there is none, as much field flows into any small region as flows out.
It is the first of Maxwell's four equations.
Symbol by symbol
| Symbol | Say it | Means |
|---|---|---|
| ∇ · | the divergence of | how much a field spreads out from a point |
| E | E | the electric field |
| ρ | rho | the charge density |
| ε₀ | epsilon naught | the permittivity of free space |
More on∇Nabla (del)ρRhoεEpsilon
Where you meet it
Electromagnetism courses.
Questions
How do you say Gauss's law out loud?
∇ · E = ρ / ε₀ is read: “the divergence of E equals rho over epsilon naught.” That is exactly what Aethel says when it meets the formula in a book.
What does ∇ · mean in Gauss's law?
∇ · (said “the divergence of”) is how much a field spreads out from a point.
What does E mean in Gauss's law?
E (said “E”) is the electric field.
Can I listen to the equations in my own textbook like this?
Yes. Upload a PDF, EPUB or text file and Aethel reads it aloud with every equation spoken as maths, the way it reads this one, and highlights each sentence as it goes. You can start free.