Electric Flux Through Open and Closed Surfaces: Comparison Problems
Electric-flux questions often look similar but depend on one crucial distinction: Is the surface open or closed? This guide compares the cases students most often confuse — surface orientation, area vectors, enclosed charge, external charge, hemispheres and zero-flux situations — so that you can decide the correct method before calculating.
Start by Identifying the Type of Surface
Open Surface Formula vs Gauss’s LawFor a flat open surface of area A in a uniform electric field E, the electric flux is
Φ = EA cos θ
where θ is the angle between the electric field vector and the area vector, which is normal to the surface.
For a closed surface, the net electric flux is
Φclosed = E · dA = Qenclosed/ε0
Open Surface vs Closed Surface
The First Decision in Every Flux ProblemCalculate flux through that surface using E⃗ · dA⃗, symmetry or a suitable integral.
For total net flux, Gauss’s law gives Q enclosed / ε0 directly.
Gauss’s law gives total flux; symmetry or subtraction is needed to obtain one part.
It may produce field on the surface, but its net contribution to closed-surface flux is zero.
Electric Flux Comparison Problems
Compare Before You CalculateComparison 1: Same Area, Different Orientation
Two identical flat surfaces of area A are placed in the same uniform electric field E. For Surface 1, the area vector is parallel to E. For Surface 2, the area vector makes 60° with E.
Φ1 = EA cos 0° = EA
Φ2 = EA cos 60° = EA/2
Therefore, Φ1 = 2Φ2. The surface area is the same; only orientation changes the flux.
Comparison 2: Same Closed Surface, Charge Inside vs Charge Outside
Case A: a point charge q is inside a closed surface.
Case B: the same charge q is outside the same closed surface.
Case A: Φ = q/ε0
Case B: Φ = 0
In Case B, the external charge can still create a nonzero electric field at points on the surface. Field lines entering the surface are balanced by field lines leaving it, so the net flux is zero.
Comparison 3: Charge at the Centre of a Sphere vs Same Charge Off-Centre
A charge q is first placed at the centre of a closed spherical surface and then moved to another point inside the sphere.
Φcentre = q/ε0
Φoff-centre = q/ε0
The total closed-surface flux is unchanged because the enclosed charge is unchanged. What does change is the distribution of flux over different parts of the sphere.
Comparison 4: Curved Hemisphere vs Full Sphere
A point charge q is placed at the centre of a sphere. Compare the flux through the full spherical surface with the flux through one curved hemispherical half.
Φsphere = q/ε0
Φhemisphere = q/(2ε0)
Because the charge is at the centre, spherical symmetry divides the total flux equally between the two curved hemispherical halves. The factor 1/2 comes from symmetry.
Comparison 5: Closed Surface with +q and −q Inside
A closed surface encloses two equal and opposite point charges +q and −q.
Qenclosed = +q − q = 0
Φnet = 0
This does not mean the electric field is zero on the surface. The fields of the two charges may be substantial, but the total outward and inward flux cancels.
Comparison 6: One Face of a Cube vs the Whole Cube
A point charge q is placed at the centre of a cube.
For the entire cube:
Φcube = q/ε0
By symmetry, all six faces receive equal flux:
Φone face = q/(6ε0)
The factor 1/6 comes from symmetry, not directly from Gauss’s law.
Positive, Negative and Zero Electric Flux
Read the Direction of E · dAE has a component in the same direction as the outward area vector; field lines leave the surface.
E has a component opposite to the outward area vector; field lines enter the closed surface.
E is tangent to the surface, so E is perpendicular to dA and cos 90° = 0.
Net enclosed charge is zero; local electric field need not be zero.
Common Electric Flux Traps
Check the Wording Before the FormulaFlux uses the angle between E and the area vector, not between E and the surface itself.
Gauss’s law gives total flux only through a complete closed surface.
Only charge geometrically inside the closed surface appears in Q enclosed.
Electric field can be nonzero even when inward and outward flux cancel.
Equal sharing between faces or halves requires a symmetric charge position and geometry.
For closed surfaces, dA always points outward.
A Fast Comparison Checklist
Use Before Solving2. Is the question asking for local flux or net closed-surface flux?
3. What is the direction of the area vector?
4. Is the given angle measured from the surface or from its normal?
5. What net charge is actually enclosed?
6. Is symmetry strong enough to divide total flux equally among parts?
Continue with Electric Flux and Gauss Law Practice
Free PhysicsGurukul ResourcesThis page focuses on comparison and decision-making. Use the existing numerical sets below for broader calculation practice.
Area vectors, orientation, vector dot products and Gauss-law flux questions. → GAUSS Numerical Problems on Applications of Gauss’s Law
Practise field calculation for highly symmetric charge distributions. → PG-061 When Gauss Law Simplifies an Electric Field Problem
Learn when symmetry makes Gauss’s law useful for finding E. → CLASS 12 CBSE Class 12 Study Materials 2026–27
Return to the current Class 12 resource hub. →
Electric Flux in the CBSE Class 12 Physics Syllabus 2026–27
Chapter 1 • Electric Charges and FieldsElectric flux, Gauss’s theorem and its applications remain part of Chapter 1: Electric Charges and Fields in the current CBSE Class 12 Physics syllabus. The prescribed applications include an infinitely long straight wire, a uniformly charged infinite plane sheet and a uniformly charged thin spherical shell.
Frequently Asked Questions
Electric Flux • Open & Closed SurfacesWhat is the difference between electric flux through an open surface and a closed surface?
For an open surface, flux depends on the electric field, area and orientation of that particular surface. For a complete closed surface, the net flux is related to the net enclosed charge by Gauss’s law.
Can Gauss’s law be applied directly to an open surface?
No. Gauss’s law in the form Φ = Q enclosed / ε0 applies to the total flux through a closed surface. Flux through an open portion must be found using E · dA, symmetry or by subtracting known fluxes.
Can electric flux be negative?
Yes. Flux is negative when the electric field has a component opposite to the chosen area vector. For a closed surface, an inward field component gives negative local flux.
Does zero net flux imply zero electric field?
No. Zero net flux only means that the net enclosed charge is zero. The electric field may still be nonzero on the surface.
If a charge is moved inside a closed surface, does the total flux change?
No, as long as the charge remains inside and the net enclosed charge stays the same. The distribution of flux over different parts of the surface may change, but the total remains q/ε0.
Why is the flux through one face of a cube q/(6ε0) when a charge is at the centre?
Gauss’s law gives the total flux q/ε0 through the cube. Because the charge is at the centre and all six faces are equivalent by symmetry, the total flux is shared equally among them.
