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Physics · lesson 1 of 4

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.

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Prerequisites: Vector fields, dot products and surface integrals.

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.

Worked examples

Example 1

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

Flux EA cos(0)=12.

12 N m²/C

Example 2

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

The enclosed algebraic charge controls total flux.

Net enclosed charge

Check your understanding

8 questions

Decimals or fractions are accepted for numeric answers. Proofs and written responses use sample answers and require human marking. This is practice, not a protected examination.

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

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12 N m²/C

Flux EA cos(0)=12.

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

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Net enclosed charge

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.

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5

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?

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No; contributions can cancel

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 and 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.

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.N m²/C

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5 N m²/C

Multiply EA by cos 60°=1/2.

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

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A sphere centred on the charge

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 and marking guidance

Without enough symmetry, the surface integral provides an integral constraint but does not isolate the unknown field distribution.

Credit symmetry and field variation.

Further reading and review references

These are reference links, not copied exercises, institutional endorsement or proof of independent review.