The Electric Field of a Continuous Charge Distribution · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Adding up the push of many charges

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

  1. The field of a positive point charge points away from it and weakens with distance squared.

    Circle one:   True   False

  2. How is the electric field at a point defined?

    • Force on a tiny positive test charge divided by its charge
    • Total charge of all nearby objects added together
    • Distance from the nearest charge alone

  3. What does charge per unit length describe?

    • The total voltage of a battery
    • How charge spreads along a line
    • The mass of each electron

  4. Why do sideways components vanish on the axis of a charged ring?

    • Opposite sides push sideways in opposite ways and cancel
    • Charge on a ring never pushes sideways
    • The test charge absorbs sideways pushes

  5. How do you set up the field of a charged rod?

    • Treat the whole rod as one electron
    • Chop it into point pieces and integrate their contributions
    • Measure the field only at the rod center

  6. Your rod integral gives a field that grows with distance far away. What should you conclude?

    • The result is correct, since fields grow far away
    • Something is wrong, since it should fade like a point charge
    • Far away checks never apply to rods

  7. A sheet of charge needs its field at a nearby point. Which density belongs in the integral?

    • Charge per unit length
    • Charge per unit temperature
    • Charge per unit area

  8. A student adds the magnitudes of two charge contributions that point in different directions. What is the mistake?

    • Fields add as vectors, so direction matters and parts can cancel
    • Fields can never be added together at all
    • Magnitudes always add, so the student is right
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Answer key

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

Adding up the push of many charges W1-mt_IIcVqWapC1-s1

  1. True · Like charges repel, and the push spreads over distance squared.
  2. Force on a tiny positive test charge divided by its charge · The field is the per charge push a test charge would feel there.
  3. How charge spreads along a line · Linear density tells how much charge each tiny length piece carries into the integral.
  4. Opposite sides push sideways in opposite ways and cancel · Symmetry pairs every sideways push with an equal opposite one, leaving only the axis part.
  5. Chop it into point pieces and integrate their contributions · Each tiny piece contributes like a point charge, and the integral adds them all.
  6. Something is wrong, since it should fade like a point charge · From far away any shape looks pointlike, so the field must fade the point charge way.
  7. Charge per unit area · Sheets chop into area patches, so each patch holds surface density times its tiny area.
  8. Fields add as vectors, so direction matters and parts can cancel · The total field is the vector sum, and ignoring direction misses cancellations.
Worksheet · LightMySky