Final answer:
True statements about electric field lines are: they can never cross, the density of field lines is proportional to the electric field strength, and this density is not proportional to local charge density. Charged particles do not always move along field lines, and field lines can exist without local charges. The statements which are true: A, D and E.
Step-by-step explanation:
Regarding the properties of electric field lines, the true statements are:
- A. Electric field lines can never cross over one another. This is because if two field lines crossed, that location would have two different directions of the electric field, which is not possible as the electric field at a point is unique.
- D. The density of field lines at a point is proportional to the strength of the electric field. This means that the closer the lines are to each other, the stronger the electric field is at that point.
- E. The density of field lines at a point is not directly proportional to the charge density but rather proportional to the magnitude of the charge that is producing the field lines. The number of lines is proportional to the magnitude of the charge, which also indicates the field's strength.
The other statements B and C are not true. The motion of a charged particle will not always follow exactly on a field line since the particle may have initial velocity components that are not along the electric field line. Also, field lines can exist in regions of space where there are no charges as they can extend to infinity or from distant charges.