Electric flux is a concept in electrostatics that helps us understand the flow of electric field lines through a closed surface. It is a way to quantify how many electric field lines pass through a given area. Electric flux (
Φ
Φ
E
) is defined mathematically as:
Φ
=
⋅
⋅
cos
(
)
Φ
E
=E⋅A⋅cos(θ)
Where:
Φ
Φ
E
is the electric flux.
E is the electric field vector.
A is the area vector of the surface.
θ is the angle between the electric field vector and the normal vector of the surface.
In simple terms, the electric flux through a closed surface is proportional to the number of electric field lines passing through that surface. If the electric field lines are perpendicular to the surface (
=
0
θ=0), the electric flux will be at its maximum. If the electric field lines are parallel to the surface (
=
9
0
∘
θ=90
∘
), the electric flux will be zero because no field lines are passing through the surface.
Mathematically, for a more general case where the electric field may not be uniform across the surface, you can integrate the dot product of the electric field (
E) and the differential area (
dA) over the entire closed surface (
S):
Φ
=
∬
⋅
Φ
E
=∬
S
E⋅dA
In cases where the electric field is uniform and the surface is flat and perpendicular to the field lines, the formula simplifies to:
Φ
=
⋅
Φ
E
=E⋅A
Where:
E is the magnitude of the electric field.
A is the area of the surface.
Electric flux is a useful concept in various electrostatics applications, such as Gauss's law, which relates the electric flux through a closed surface to the charge enclosed by that surface. It's important to note that electric flux is a scalar quantity and is measured in units of electric field times area (e.g., N·m²/C or V·m).