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Electricity & Magnetism

Charges & Electric Fields

What one charge does to the space around it, and why a field line is a map of directions, never a track to run along.

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Charges & Electric Fields

What one charge does to the space around it, and why a field line is a map of directions, never a track to run along.

30 min3 checkpoints5 simulation tasks

Introduction

Two charges pull on each other across empty space, with nothing connecting them.

Predict

Directly below a positive charge, the field line runs straight down. A positive test charge there is launched to the right at 6 m/s. What path does it take?

A field line is not a track

Try it

Run it and watch the charge leave its field line. Then change the launch so it stays on the line.

GoalKeep the charge on its field line for a whole run.

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The sign of the charge you bring

Predict

A dipole: + on the left, − on the right. Above the midpoint the field points right. A negative test charge is released there from rest. Which way does it move?

Try it

Run it: the rose force arrow F points against the indigo field arrows. Now make F point along the field, without moving the source charges.

GoalMake the force point along the field.

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A point charge qsq_s fills the space around it with a field, a vector at every point whether or not anything is there:

E⃗=14πε0 qsr2 r^\vec{E} = \frac{1}{4\pi\varepsilon_0}\,\frac{q_s}{r^2}\,\hat{r}

pointing away from a positive source, toward a negative one. A charge qq placed there feels F⃗=q E⃗\frc{\vec{F}} = q\,\vec{E}: the field belongs to the source, the force to the pair.

Practice

A point charge of nC sits 2.5 m directly above a point. What is the field strength at that point?

Where the field cancels, and where it does not

Predict

Two equal positive charges sit 2 m apart. What is the electric field in the region between them?

Try it

Two equal positive charges, and a test charge just above the midpoint. Move it to the one point where the field is zero.

GoalPark the test charge where the field is zero.

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Fields add as vectors, which is called superposition. Nothing wins and nothing is used up. Between two equal like charges the vectors cancel at one point only, and everywhere else the field is not zero.

Practice

Two charges of nC each sit 2 m apart. What is the field strength m above their midpoint?

Energy, and what is being spent

Predict

The positive test charge is fired straight at the positive source, at 3 m/s. Sketch its kinetic energy until it leaves the map.

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Try it

Now get the charge to within 1 m of the source. How fast does it have to be launched?

GoalGet the charge within 1 m of the source.

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Kinetic energy trades with the potential energy U=qVU = qV, where VV is the electric potential, a number at every point: for a point charge, V=kqs/rV = kq_s/r. Their total never moves, because the electric force is conservative. A charge accelerating across a field spends potential energy, never charge.

Practice

A 1 nC test charge sits m from a nC point charge. What is its potential energy?

What comes next

You watched a charge leave its field line, reversed a force without touching the field, and traded kinetic energy for potential energy. Next: divide the energy by the charge, instead of the force, and you get a single number at every point, with no direction to track. That number is the potential, and it is why circuits are discussed in volts.

Ideas this lesson took on

Each of these is a common intuition the lesson put to the test. If one still feels right, the section that tests it is worth another look.

  • “A charge follows the field line it starts on”
  • “A negative charge is pushed along the field, the same way a positive one is”
  • “The field is zero everywhere between two equal charges”
  • “Two charges use up their field pushing on each other”

Finished with this lesson?

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Research behind this lesson

  • Campos et al. 2019: How students read the electric-field-line diagram feeds directly into how they apply superposition: the study found evidence that an incorrect interpretation of the field-line diagram hinders understanding of the superposition principle for the electric field.
  • Maloney et al. 2001: The Conceptual Survey of Electricity and Magnetism (CSEM): a 32-question multiple-choice instrument refined over four years and administered to more than 5000 introductory students at 30 institutions. Pretest averages were 31% (calculus-based) and 25% (algebra/trigonometry-based); after instruction they reached only 47% and 44%.
  • Törnkvist et al. 1993: Shown canonical electric-field-line diagrams and asked to give the force on, and the trajectory of, a test charge, students did not hold apart the field line, the force vector, the velocity vector and the trajectory: the single drawn line was read as all four at once.