Gauss's law
The total electric flux through a closed surface equals the enclosed charge divided by epsilon zero.
Last updated
Analogy
Counting how many arrows leave a balloon to learn how much charge is inside.
Example
flux = Q / epsilon0= 1e-9 / 8.85e-12= 113 N m^2/C
In practice
A 1 nC charge inside any closed surface gives a flux of about 113 N m squared per C.
Practice
Flashcards
- What does Gauss's law connect?Electric flux through a closed surface and the charge inside.
Interview questions
- Use Gauss's law to find the field outside a charged conducting sphere of charge Q and radius R.
- Choose a spherical surface
- Field is the same size everywhere on it
- E x 4 pi r^2 = Q / epsilon0 gives E = kQ/r^2
Questions people ask
When is Gauss's law useful?
It is easiest when charges are spread in a symmetric shape, such as a sphere, a long line or a flat sheet. Then you can choose a surface where the field is constant and perpendicular, which turns flux into field times area. For messy shapes, you need other methods.
What is electric flux?
Flux measures how much field passes through a surface, calculated as E times area times cosine of the angle between the field and the surface's normal. Its unit is N m squared per C. A field running parallel to the surface gives zero flux, while a field straight through gives maximum.