Recovering the Field from the Potential Gradient · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading the field off a voltage map

Science · Electricity & Magnetism · ages 19-20
Name ______________________   Date ____________

  1. How do electric field lines meet equipotential surfaces?

    • At right angles, from high toward low
    • Along the surface, never crossing
    • At right angles, from low toward high

  2. The potential rises with slope 4 V/m along x. What is E_x?

    • +4 V/m
    • -4 V/m
    • 0 V/m

  3. The potential is flat along y in some region. What is E_y there?

    • Maximum
    • Zero
    • Equal to the potential

  4. Neighbouring equipotential lines differ by 10 V and sit 2 m apart. What is the field there?

    • About 20 V/m toward the higher line
    • About 12 V/m along the lines
    • About 5 V/m toward the lower line

  5. A point charge has V = kQ over r. What field do you recover?

    • kQ over r squared, pointing inward
    • kQ over r squared, pointing outward
    • kQ over r cubed, pointing outward

  6. No work is done moving a charge along an equipotential.

    Circle one:   True   False

  7. Between parallel plates at fixed field, the gap doubles. What happens to a charge's energy gain crossing it?

    • It halves
    • It stays the same
    • It doubles

  8. Jo computes the slopes correctly but skips the minus sign, pointing E uphill. What is wrong?

    • The field aims down the steepest drop, so the sign must flip
    • Slopes must be measured along equipotentials
    • The field equals the potential itself
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Answer key

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

Reading the field off a voltage map W1-mt_EqCLB9bqG1-s1

  1. At right angles, from high toward low · Field lines cross equipotentials squarely, running downhill.
  2. -4 V/m · Each component is the slope with a flipped sign.
  3. Zero · A flat slice has zero slope, so the component vanishes.
  4. About 5 V/m toward the lower line · Divide the step by the gap: 10 over 2 is 5, facing downhill.
  5. kQ over r squared, pointing outward · dV/dr is minus kQ over r squared, and E flips it back.
  6. True · Start and finish share the same potential energy.
  7. It doubles · Drop = field times distance, and gain = charge times drop.
  8. The field aims down the steepest drop, so the sign must flip · E is minus the gradient, never the bare slope.
Worksheet · LightMySky