There are two main approaches to drawing the electric field vectors:
- Vector addition of the known electric fields due to each source;
- Computing the gradient of the potential, if known, for the given configuration.
When working through § {Activity: Drawing Electric Fields}, some things that you might have needed to pay attention to are:
- The electric field is a vector field, not a scalar field, i.e. it is a vector at every point in space, not a scalar. Make sure to add the vectors themselves, not their magnitudes.
- Typically, zero potential does not correspond to zero electric field and vice versa.
- These examples are inherently 3-dimensional; drawing vector fields in three dimensions may be more challenging than visualizing the three dimensional fields in your head.
Electric field lines are another representation of electric fields. They satisfy the following properties:
- Field lines start at positive charges and end at negative charges;
- Field lines are tangent to the direction of the electric field at each point (i.e. the direction of the field lines is the same as the direction of the electric field at each point). As a consequence of this, field lines never cross.
- The density of field lines is proportional to the strength of the electric field in that area. Be cautious in trying to represent the electric field in terms of field lines. In particular, drawing electric field lines in two dimensions will not show the correct density everywhere; it requires electric field lines in three dimensions to see the correct fall off.