# Electric flux and Gauss symmetry

> Electric flux is the oriented surface integral of E·dA. A negative flux reflects direction relative to the chosen normal, not negative area.

Course: [Fields, circuits and thermal physics](https://studybrix.com/en/courses/fields-and-thermal-physics/index.md)
Level: university
Prerequisites: Vector fields, dot products and surface integrals.

## Notes

### Flux

Electric flux is the oriented surface integral of E·dA. A negative flux reflects direction relative to the chosen normal, not negative area.

### Gauss law

For a closed surface, total electric flux equals enclosed charge divided by ε0. Charges outside can affect the local field but not net enclosed charge.

### Symmetry

Gauss law always holds classically, but extracting E from it easily requires useful symmetry. Do not assume E is constant on an arbitrary Gaussian surface.

### Conductors

In electrostatic equilibrium the electric field inside an ideal conductor material is zero. Cavities require separate reasoning about enclosed charges.

## Practice questions

### 1. A uniform field of 4 N/C is parallel to a planar area's outward normal. For area 3 m², find flux.

Answer: 12 N m²/C

Explanation: Flux EA cos(0)=12.

### 2. What charge enters the right side of Gauss law for a closed surface?

A. Net enclosed charge
B. Only charge on the surface
C. Only positive charge inside
D. All charge in the universe

Answer: Net enclosed charge

Explanation: The enclosed algebraic charge controls total flux.

### 3. Use ε0=2 in stated model units. A closed surface encloses charge 10. Find total electric flux in the matching units.

Answer: 5

Explanation: Gauss law gives Qenclosed/ε0=10/2; the units are deliberately rescaled.

### 4. Does zero net flux imply zero electric field at every point on the surface?

A. Yes, in every geometry
B. Only if charge exists outside
C. Yes, if the area is nonzero
D. No; contributions can cancel

Answer: No; contributions can cancel

Explanation: A uniform external field can enter and leave a closed surface with zero net flux.

### 5. Explain why a point charge outside a Gaussian surface can affect E without changing its total flux.

Sample answer / marking guidance: It contributes a local field, but its field lines enter and leave the closed surface with cancelling oriented contributions. It adds no enclosed charge.

Explanation: Credit the distinction between field and integral flux.

### 6. A field makes an angle of 60 degrees with the normal. If EA=10 N m²/C, find flux.

Answer: 5 N m²/C

Explanation: Multiply EA by cos 60°=1/2.

### 7. Which geometry offers the appropriate symmetry for an isolated point charge?

A. A line segment
B. An arbitrary open disk
C. A sphere centred on the charge
D. Any displaced cube with constant E assumed

Answer: A sphere centred on the charge

Explanation: On the centred sphere E is radial with constant magnitude.

### 8. State one reason why Gauss law alone does not make every electrostatic field problem elementary.

Sample answer / marking guidance: Without enough symmetry, the surface integral provides an integral constraint but does not isolate the unknown field distribution.

Explanation: Credit symmetry and field variation.

## Further reading

- https://ocw.mit.edu/courses/8-09-classical-mechanics-iii-fall-2014/
- https://openstax.org/details/books/university-physics-volume-3

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.