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Electric flux and enclosed charge

Science · Electricity & Magnetism · ages 18-19

Name ______________________ Date ____________

A flat patch in a uniform electric field has zero flux when the field is parallel to the patch.
Circle one: True False
What does electric flux measure?
- Signed electric field crossing a chosen surface
- Total electric charge distributed over a chosen surface
- Average speed of charged particles passing through a wire
For a closed surface, what sign does an inward electric-field contribution to flux have?
- Positive
- Negative
- Zero
According to Gauss's law, what equals the net outward electric flux through a closed surface? No charge lies on its boundary.
- Net charge inside and outside divided by ε0
- Total unsigned enclosed charge divided by ε0
- Net enclosed charge divided by ε0
A uniform electric field has strength 40 N/C. A flat patch has area 0.5 m². Its chosen normal makes a 60° angle with the field. Using cos60° = 0.5, what is the flux?
- 0 N·m²/C
- 20 N·m²/C
- 10 N·m²/C
A point charge is outside a closed box. What contribution does that charge make to the box's net outward electric flux?
- Its charge divided by ε0, as though it were enclosed
- Zero net flux, though the field can change
- Twice its charge divided by ε0 for entry and exit
A uniformly charged, infinitely long straight line is alone in space. Which closed Gaussian surface lets you find its electric field most directly using symmetry?
- A closed cylinder coaxial with the line
- A closed sphere centered at a point on the line
- A closed cube centered at a point on the line
A student expects triple the flux after tripling the radius of a sphere centered on an isolated positive point charge. The charge stays fixed. What actually happens to the total outward flux?
- It remains at its original value
- It becomes nine times its original value
- It becomes one ninth of its original value

Answer key

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True · The field is perpendicular to the patch's normal, so θ = 90°. Since cos90° = 0, Φ = EA cosθ is zero.
Signed electric field crossing a chosen surface · Flux combines the field crossing a surface with the surface area and orientation. It is not the charge on the surface or a particle speed.
Negative · Closed-surface normals point outward. An inward field has a negative component along that normal, so its flux contribution is negative.
Net enclosed charge divided by ε0 · Gauss's law gives Φ = Qenc/ε0. Qenc is the signed sum of charges inside the surface, not the sum of charge magnitudes or a sum including outside charges.
10 N·m²/C · Φ = EA cosθ = 40 × 0.5 × 0.5 = 10 N·m²/C. The 60° angle is measured from the chosen normal.
Zero net flux, though the field can change · The outside charge contributes no enclosed charge. Its inward and outward flux contributions cancel, even though it changes the field on the box.
A closed cylinder coaxial with the line · A coaxial cylinder has constant signed normal field on its curved side and zero end-cap flux. Side flux is +EA for positive line charge or -EA for negative line charge, with E the field strength and A the side area.
It remains at its original value · Tripling radius multiplies sphere area by 9 and divides field strength by 9. Their product is unchanged, consistent with the same enclosed charge.