Electric flux is a measure of the electric field passing through a surface. It quantifies the amount of electric field lines that pass through a given surface. The electric flux (
Ī¦
Ī¦
E
ā
) through a closed surface is calculated using Gauss's law, which relates the electric flux to the total enclosed electric charge (
Q) by the equation:
Ī¦
=
0
Ī¦
E
ā
=
Īµ
0
ā
Q
ā
,
where:
Ī¦
Ī¦
E
ā
is the electric flux through the closed surface.
Q is the total electric charge enclosed by the surface.
0
Īµ
0
ā
is the permittivity of free space, a constant with a value of approximately
8.854
Ć
1
0
ā
12
8.854Ć10
ā12
CĀ²/(NĀ·mĀ²).
This equation is valid when the electric field is uniform and perpendicular to the surface, and the surface is closed (i.e., it completely encloses a volume of space). If the electric field is not uniform or not perpendicular to the surface, the calculation of electric flux becomes more involved, and you would need to integrate the dot product of the electric field (
ā
E
) and the infinitesimal area (
ā
d
A
) over the surface:
Ī¦
=
ā«
ā
ā
ā
Ī¦
E
ā
=ā«
E
ā
d
A
.
Here,
ā
E
is the electric field vector, and
ā
d
A
represents a differential area element of the surface. The dot product
ā
ā
ā
E
ā
d
A
ensures that only the component of the electric field perpendicular to the area contributes to the flux.
In cases where the electric field is constant and the surface is uniform and flat, the integral simplifies to:
Ī¦
=
ā
Ī¦
E
ā
=Eā
A,
where:
E is the magnitude of the electric field.
A is the area of the surface perpendicular to the electric field.
In more complex scenarios where the electric field varies across the surface or is not perpendicular to the surface, the integration becomes necessary to accurately calculate the electric flux.