K323 / 2027
Static electricity overview

Topic 4 of 5

Electric fields and force direction

An electric field is a region in which an electric charge experiences a force. A field diagram describes the effect of the source charges at different positions.

Unlike charges attract and like charges repel. A field-line arrow uses one fixed convention: it points in the direction of force on a positive test charge.

Draw the required point-charge patterns

A point-charge model treats the source's size as negligible compared with the distances being considered. For the test-charge interpretation, imagine a charge small enough not to change the source arrangement significantly.

A field arrow gives the force direction on a positive test charge

These are schematic field lines, not visible threads or particle tracks. Lines that reach a frame continue beyond the drawing. Their number is not a supplied measure of field strength.

One isolated positive charge

One isolated positive chargeEight radial field lines point outwards from the positive point charge. Lines that reach the frame continue outside this drawing. Arrow direction represents force on a positive test charge.+Frame marks the edge of the drawing

One isolated negative charge

One isolated negative chargeEight radial field lines point inwards towards the negative point charge. This has the same radial shape as the positive pattern but the arrows are reversed. Arrow direction represents force on a positive test charge.-Frame marks the edge of the drawing

Equal unlike charges

Equal unlike chargesField lines leave the positive charge on the left and enter the negative charge on the right. Curved lines do not cross. Some parts of the pattern lie beyond the drawing window; a line reaching the frame is not ending in empty space. Arrow direction represents force on a positive test charge.+-Frame marks the edge of the drawing

Two equal positive charges

Two equal positive chargesField lines leave both positive charges and curve away from the region between them. They do not connect one positive charge to the other and do not cross. All displayed lines reaching the frame continue outside the drawing. Arrow direction represents force on a positive test charge.++Frame marks the edge of the drawing

Two equal negative charges

Two equal negative chargesThe pattern has the same shape as the two-positive-charge pattern, with every arrow reversed. Lines enter each negative charge, do not join negative to negative and do not cross. Arrow direction represents force on a positive test charge.--Frame marks the edge of the drawing
Arrows leave positive point charges and enter negative point charges. Unlike charges have connecting lines directed from positive to negative. Like charges have lines that bend away from the region between them rather than joining like signs.
One isolated positive charge
Draw radial lines pointing outwards. A positive test charge is repelled from the source.
One isolated negative charge
Draw radial lines pointing inwards. A positive test charge is attracted towards the source.
Two equal unlike charges
Lines run from the positive charge towards the negative charge, with curved lines above and below the line joining them. Arrowheads must agree with the positive-test-charge convention.
Two equal positive charges
Lines leave both charges and curve away from the middle region. They do not connect positive to positive.
Two equal negative charges
The pattern has the corresponding shape to two equal positive charges, with arrows reversed to point into the negative charges.

Field lines do not cross: crossing would give two different field directions at one position. Lines may leave the edge of a diagram to represent a field extending beyond the drawing; they should not simply end at an unlabelled point in empty space. At a position where the resultant field is zero, there is no nonzero field-direction arrow to draw.

The lines are a representation, not visible threads around the charges. Their drawn number is not a count of particles. Do not infer an exact numerical field strength by counting an illustrator's lines.

A negative charge has the opposite force direction

Keep the field direction fixed when changing the test charge

Green arrows show the supplied field; orange arrows show electric force. Blue arrows or paths show motion. A force direction need not be the current direction of motion.

A rightward field gives opposite forces on positive and negative test chargesOne supplied field points right. In two separate test-charge examples, a positive charge has a rightward electric force and a negative charge has a leftward electric force. The field arrow does not reverse when the test charge is changed. Orange force arrows belong to their labelled test charge and do not show velocity.Supplied field+Force on positive charge: right-Force on negative charge: left

Apply the same rule to a particle separator

Upward-moving opposite charges deflect to opposite sides in a leftward fieldA supplied electric field points left. Two otherwise identical particles enter moving upwards, a positive one on the left and a negative one on the right. The electric force on the positive particle points left; the force on the negative one points right. Dashed blue qualitative paths curve upwards to their respective sides. Both particles initially continue upwards while accelerating sideways. Gravity and air resistance are ignored. No numerical field, speed, displacement or force scale is supplied.Supplied field: left+-Force leftForce rightBoth enter moving upwardsDashed paths show qualitative deflection

The field changes sideways motion. It does not instantly replace the particles' upward motion. Gravity and air resistance are ignored in this comparison.

In the rightward-field example, positive and negative test charges have opposite electric forces. In the separate separator example, both kinds initially move upwards through a supplied leftward field; their electric forces are horizontal and opposite.

Read the convention

The field arrow points right at a marked point

  • A positive test charge has electric force right.
  • A negative test charge has electric force left.

Changing the test-charge sign reverses its force. It does not reverse the existing field established by the source charges.

Force changes motion; it does not specify the velocity an object already has. A charge moving left can experience force right, so it may initially slow before reversing. If electric force is the only unbalanced force, its direction gives the acceleration direction, consistent with resultant force and acceleration.

Apply a supplied field to a new arrangement

In the separator diagram, positive and negative particles enter moving upwards. The field points left. Ignore gravity and air resistance for this comparison.

The positive particles experience force left and begin to bend towards a left collector. Negative particles experience force right and begin to bend towards a right collector. Both initially continue moving upwards while their horizontal velocities change. The force does not instantly turn either velocity through a right angle.

A field line is not automatically a moving particle's path. It shows force direction for a positive test charge at each point. The charge's sign, existing velocity and other forces also matter when predicting its motion.

Optional check An existing electric field points to the right at a marked position. A small negative test charge is placed there without significantly changing the field. Which statement is correct?
An existing electric field points to the right at a marked position. A small negative test charge is placed there without significantly changing the field. Which statement is correct?