Electric flux is a concept in electromagnetism that helps us understand the flow of electric field lines through a closed surface. It's a way to quantify the "effectiveness" of an electric field in penetrating or passing through a given surface. Electric flux is defined mathematically as the dot product of the electric field vector and the area vector of the surface, integrated over that surface.
Mathematically, the electric flux (
Φ
Φ
E
) through a closed surface
S is given by the integral:
Φ
=
∫
⋅
Φ
E
=∫E⋅dA
Where:
Φ
Φ
E
is the electric flux.
E is the electric field vector.
dA is an infinitesimal area vector on the surface
S.
The dot product
⋅
E⋅dA represents the component of the electric field that is perpendicular to the infinitesimal area
dA. When the electric field and the area vector are aligned (i.e., when the angle between them is zero), the dot product is at its maximum, and when they are perpendicular (angle of 90 degrees), the dot product is zero. This captures the idea that the electric field lines that are perpendicular to the surface contribute the most to the electric flux.
If the electric field is not uniform or the surface is not flat, the integral needs to be calculated over the entire closed surface to determine the total electric flux passing through it.
The SI unit of electric flux is the volt-meter (
⋅
V⋅m or
⋅
2
⋅
−
1
N⋅m
2
⋅C
−1
).
Electric flux is an important concept in Gauss's law, which is one of Maxwell's equations. Gauss's law relates the electric flux through a closed surface to the charge enclosed by that surface. It helps us understand how electric charges create electric fields, and how those fields interact with surfaces and volumes.