Electric Flux and Gauss's Law · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Counting field lines through a surface

Science · Electricity & Magnetism · ages 18-19
Name ______________________   Date ____________

  1. A flat patch edge on to a uniform field catches zero flux.

    Circle one:   True   False

  2. What does electric flux count?

    • How much field passes through a surface
    • How many charges sit on a surface
    • How fast charges move inside a wire

  3. For a closed surface, which sign does entering field carry?

    • Positive
    • Negative
    • It carries no sign at all

  4. What does the law say the total flux out of any closed surface equals?

    • The total charge anywhere in the universe
    • The surface area times the volume
    • The inside charge divided by the vacuum permittivity

  5. How do you handle flux through a curved surface?

    • Chop it into tiny flat pieces and add them up
    • Measure only the single flattest point
    • Multiply the total volume by the field

  6. A charge sits outside your closed box. What does it contribute to the total flux?

    • The full charge divided by permittivity
    • Nothing net, since its lines enter and leave
    • Double the usual amount

  7. An empty closed box sits in a uniform field. What is its total flux?

    • Zero, since as much enters as leaves
    • Field times volume of the box
    • Field times the longest edge

  8. A student doubles the radius of a sphere around a point charge and expects double the flux. What is wrong?

    • Nothing, flux grows with radius
    • Flux ignores size: area growth cancels field fading
    • Flux only works for tiny spheres
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Counting field lines through a surface W1-mt_Z5dZQvik6o-s1

  1. True · No field lines cross an edge on patch, so the cosine factor gives zero.
  2. How much field passes through a surface · Flux is the measure of field flow through the chosen area.
  3. Negative · Entering counts negative while leaving counts positive, so pass through cancels.
  4. The inside charge divided by the vacuum permittivity · Only enclosed charge matters, scaled by one over the vacuum permittivity.
  5. Chop it into tiny flat pieces and add them up · Each tiny piece is nearly flat, so the flat rule applies piece by piece.
  6. Nothing net, since its lines enter and leave · Outside lines that enter must also exit, and the signs cancel.
  7. Zero, since as much enters as leaves · No charge inside means the law gives zero, matching the enter leave cancel.
  8. Flux ignores size: area growth cancels field fading · Area grows with distance squared while the field fades the same way.
Worksheet · LightMySky