Episode 406: Fields field lines and equipotentials

This episode introduces fields, field lines and equipotentials in the context of electric fields. Much of this is revision from g-fields, but with the slight added twist of needing to take account of the sign of charge when examining electric fields.

Summary

  • Discussion and demonstration: Field lines (20 minutes)
  • Discussion and student experiment: Equipotentials (35 minutes)
  • Student questions: Field lines and equipotentials (10 minutes)

Discussion and demonstration: Field lines
Electrical charges exert forces upon one another. Just as with gravity, these forces can be understood in terms of fields that exist between ‘charged’ particles.

What is the basic law of force between charges? (Like charges repel, unlike charges attract.)

How do these forces occur if, as usual, the charges are not in contact? (The presence of electric fields between the charges. A field is set up by a charge, and any other charge in that field will experience a force due to the field.)

How do we usually represent these fields? (With field lines or lines of force.)

Now we have to be careful with our use of field lines to represent electrical fields. In the gravitational field all forces are attractive and so putting a direction on the field line is unambiguous – it gives the direction a mass will feel a force at a point in a field. Because both attraction AND repulsion can occur in an electric field, we introduce the following convention that is consistent with the fact that only one type of mass exists, i.e. ‘positive mass’:

The direction of a field line in the electric field is the direction of the force on a small positive charge.

Thus if a positive charge is placed at a point in a field, it will feel a force in the direction of the field line at that point, but if a negative charge is placed there, it will feel a force in the opposite direction to the direction of the field line at that point.

We can see the field lines for certain geometries of charge using a simple demonstration with semolina powder in oil, between two electrodes connected to a high voltage supply.

Episode 406-1: Demonstration – electric field lines (Word, 74 KB)

This allows us to visualise the following fields: 

Field lines

Again, there are some basic rules and observations about field lines:

  • They never start or stop in empty space – they stop or start either on a charge or “at infinity”.
  • They never cross – if they did, a small positive charge placed there would feel forces in different directions, which could be resolved into the one true direction of the field line there.
  • The density of field lines on a diagram is indicative of the strength of the field.
  • The second diagram above also shows a point exactly between two like charges where no field exists (since the forces on a charge placed there would be exactly equal and opposite in direction). Such a point is called a neutral point.

Discussion and student experiment: Equipotentials
Exactly as with the gravitational field, we define an equipotential surface as one that joins points of equal potential in the field; in other words, no work is done in moving a charge on an equipotential surface. Although our discussion and definition of potential will be almost exactly the same as in the gravitational case, we will leave that to a later episode. For now, we just need to know that:

  1. Equipotential surfaces are perpendicular to field lines.
  2. Any electrical conductor is an equipotential surface.

As a result of (1) and (2) above, field lines always meet conductors at right angles (see the fourth field diagram in the last section).

Unlike with gravitational equipotentials there is quite a simple practical that the students can do to discover the shapes of electrical equipotentials in 2 dimensions.

Episode 406-2: Plotting equipotentials (Word, 69 KB)

Radial electric field with equipotentials

Sum up by discussing the shapes of some common fields and their equipotential lines. Note that where the field is uniform, the equipotentials are evenly spaced, but in a non-uniform field equipotentials get further apart as the field decreases in strength (see episode 408).

Electric field and equipotentials

(Note: the full lines represent the electric field and the dotted lines the equipotentials)

Student questions: Field lines and equipotentials
Episode 406-3: Fields lines and equipotentials (Word, 87 KB)

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Episode 406: Fields field lines and equipotentials (Word, 309 KB)