Question

Show, using the three rules for field lines given in Section 16–8, that the electric field lines starting or ending on a single point charge must be symmetrically spaced around the charge.

Short answer

The electric field at the same distance has the same magnitude for a specific charge. Therefore the density of the field lines is the same at the same distance from the charge.

Step-by-step solution

Concepts

The electric field lines are an imaginary path for a test charge to move.

The direction of the electric field lines shows the direction of the electric field at any location.

Explanation

The three rules are:

1. The electric field lines indicate the direction of the electric field at any point on the field line.
2. The density of field lines is proportional to the magnitude of the electric field at any location.
3. Electric field lines start on positive charges and end on negative charges.

You know the electric field at the same distance has the same magnitude for a specific charge. Therefore the density of the field lines is the same at the same distance from the charge. Hence, the electric field lines are symmetrically spaced around the charge.