Electric flux linked with a surface the number of electric lines of force cutting through a surface and measured as surface integral of electric field over that surface.
What is Electric Flux?
Electric flux can be thought of as the quantity of electric field lines that flow through a specific surface. Suppose, holding a flat sheet of paper in a windy situation.
The paper is the surface and the wind is the electric field, depending on its size and angle, tilting the paper will cause more or fewer wind lines to pass through it. The amount of electric field that “flows” through a surface is also indicated by electric flux.
Electric flux is a scalar quantity and is measured in V m.
Electric field in a region can be non-zero even though electric flux may be zero but its vice-versa is not possible.
Mathematically, electric flux is given by the formula:
ϕE = E ⋅ A = EA cosθ
Where:
ϕE is the electric flux,
E is the electric field vector,
A is the area vector (magnitude is area, direction is perpendicular to the surface),
θ is the angle between E and A.
Understanding with Examples
1.Flat Surface, Field Perpendicular (θ = 0°):
All electric field lines pass straight through the surface.
ϕE = EA → Maximum flux.
2. Flat Surface, Field Parallel (θ = 90°):
No field lines pass through the surface.
ϕE = 0 → Zero flux.
3. Curved Surface or Tilted Surface: We calculate flux through small patches and then add them up.
Electric Flux Through Closed Surfaces
We now discuss the total electric flux across a closed surface when the surface entirely encloses a space (such as a balloon).
Here comes Gauss’s Law, which connects electric flux to electric charge:
ϕE = qin / ε0
Where:
qin is the total charge enclosed inside the surface,
ε0 is the permittivity of free space (8.85 × 10−12 C2/Nm2.
This means:
The total flux depends only on the charge inside.
Charges outside the surface do not contribute to total flux.
Why is Electric Flux Important?
1.Visual Understanding of Electric Fields: Flux provides a concrete illustration of the intensity and dispersion of an electric field across a surface.
2. Gauss’s Law Foundation: Gauss’s Law, a potent tool for resolving electric field issues, particularly in symmetrical settings (such as spheres, cylinders, and planes), relies heavily on electric flux.
3. Physics and Engineering Applications: Knowledge of flux is useful in domains like electronics, electrostatics, and even electromagnetism, which is employed in sensors and antennas.
Key Points to Remember
Flux is scalar, not a vector.
Unit of electric flux: Nm²/C.
Depends on field strength, area size, and angle.
Zero net flux does not mean no field, it might just mean equal field lines enter and exit.
For non-uniform fields or curved surfaces, flux is found by integration:
ϕE = E ⋅ dA
Final Thoughts
Calculating and visualising the interaction of electric fields with surfaces is made easier by electric flux. It’s simply counting the electric field lines that flow through an object. It gets simpler to understand once we connect it to everyday phenomena like wind moving through a net.
The number of electric field lines that flow through a specific surface is known as the electric flux. It indicates the amount of electric field that is “flowing” through a region.
The basic formula is:
ϕE = E ⋅ A = EA cosθ
Where:
ϕE = electric flux
E = electric field strength
A = area of the surface
θ = angle between the electric field and the normal to the surface
The SI unit of electric flux is Newton metre squared per Coulomb (Nm²/C).
Maximum flux: When the field is perpendicular to the surface (θ = 0∘), so cos θ = 1.
Minimum flux: When the field is parallel to the surface (θ = 90∘), so cos θ = 0, hence flux is zero.
Electric field is the force experienced by a unit charge and is a vector.
Electric flux is the measure of electric field lines through a surface and is a scalar.
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