Question

Assume that electrical field lines are parallel to each other in a region in space and there is no charge in that region. How to show that the field is independent of the variables of system coordinates?

Answer 1

When electrical field lines are parallel and there is no charge in a region, the electric field is independent of the variables of the system coordinates.

Step-by-step explanation:

The statement assumes that the electrical field lines are parallel and no charge is present in a region of space. In such a case, the electric field is independent of the variables of the system coordinates.

To understand this, let's consider the properties of electric field lines:

1. Field lines must begin on positive charges and terminate on negative charges, or at infinity in the case of isolated charges.
2. The number of field lines leaving a positive charge or entering a negative charge is proportional to the magnitude of the charge.
3. The strength of the field is proportional to the closeness of the field lines, or the number of lines per unit area perpendicular to the lines.
4. The direction of the electric field is tangent to the field line at any point in space.
5. Field lines can never cross.

In the given scenario, the assumption is that there is no charge in the region, which means there are no positive or negative charges to start or terminate the field lines. As a result, the field lines in that region would be uniformly distributed with equal density, forming parallel lines.

Since there are no charges to influence the field, the density and direction of the field lines will remain constant irrespective of the system coordinates. Hence, the electric field in that region is independent of the variables of the system coordinates.