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Spot the mistake in a field sketch

Can two field lines ever cross each other?

You can now build field sketches. Other people's sketches arrive with mistakes in them, and a wrong sketch tells lies about the field. This lesson trains you to catch the three standard mistakes.

Every flawed field diagram in this topic breaks one of three rules you already have. Here are three sketches of the field in a storage room, each with one mistake.

Sketch 1: one arrowhead points up while the rest point down.

Near Earth's surface the field points straight down, so that arrow points the wrong way. Mistake 1: a wrong or missing arrow.

Sketch 2: the gaps between the lines are uneven.

You already have the spacing rule: where field lines are closer together, the field is stronger. This room's field has one strength everywhere, so the uneven spacing lies. Mistake 2: spacing that contradicts the field's strength.

Sketch 3: two lines cross.

Field lines never cross, because the force at a point can act in only one direction. Mistake 3: crossing lines.

Check any field sketch the same three ways, in turn: arrows, spacing, crossing.
CheckThe rule it rests onWhat a flawed sketch showsarrowslines follow the force direction thefield's rule givesarrows reversed, or missingspacingwhere field lines are closer together, thefield is strongerspacing that contradicts thestrengthcrossingfield lines never crosstwo lines through one point
The three checks, in order: arrows, spacing, crossing.

The diagram shows a sketch of the field in a stairwell. Which mistake does the sketch contain?

Radial sketches fail the same ways. A sketch of the field around a stone with the lines closer together far from the stone fails the spacing check, because a radial field is strongest near its source.

The table describes a sketch of the field around a negatively charged marble. Which mistake does the sketch contain?

Feature of the sketchAs drawndirectionarrows point in toward the marblelinesstraight, along radii, no two lines meetspacinglines closer together far from themarble

A sketch of the field around a positively charged cap shows straight lines along radii, arrows pointing in toward the cap, gaps widening with distance. Which mistake does the sketch contain?

Check the arrows: field lines point away from positive charge, and these point in. The arrows are wrong.

Check the spacing: gaps widening with distance fit a radial field. The spacing is right.

Check for crossing: no lines cross. That rule holds.

The sketch contains a wrong arrow direction.

The table describes a sketch of the field around a charged droplet. Which mistake does the sketch contain?

Feature of the sketchAs drawndirectionarrows point out from the droplet, whichis positively chargedlinestwo lines pass through the same pointspacinggaps widen with distance

A sketch that passes all three checks is a correct field diagram.

Your turn

In a sketch of the field around a charged bead, two field lines cross. Why can the sketch not be right?

The table describes a sketch of the field around Pluto. Which change makes the sketch correct?

Feature of the sketchAs drawndirectionarrows point out away from Plutolinesstraight, along radii, no two lines meetspacinggaps widen with distance

Three students sketch Earth's whole gravitational field. The table gives each sketch's features. Whose sketch is correct?

StudentFeatures of the sketchVeraarrows in toward Earth; gaps widen with distance; notwo lines meetIdrisarrows in toward Earth; gaps widen with distance; twolines crossCasperarrows out away from Earth; gaps widen with distance;no two lines meet