Question

assertion: the potential difference between any two points in an electric field depends only on initial and final position. reason: electric field is a conservative field so the work done per unit positive charge does not depend on path followed. True or False

Answer 1

The assertion that potential difference in an electric field is dependent only on the initial and final positions, not the path, is true because the electric field is conservative. Therefore, work done is path-independent, making electric potential a useful measure.

Step-by-step explanation:

The assertion that the potential difference between any two points in an electric field depends only on initial and final position is true. The reason provided is also true as the electric field is a conservative field. This means that work done per unit positive charge in moving from one point to another in an electric field does not depend on the path followed, thereby making electric potential a useful concept. As a conservative field, the work done or energy transferred in moving a charge within it depends only on the initial and final locations, not the path taken.

Thus, when dealing with electrostatic forces, we can define an electric potential energy for a system of charges. This potential energy is simply the work done in bringing a charge from a reference point (often at infinity) to a specific point in the field. The superposition principle allows potential energies from individual pairs of charges to be added to find the total potential energy of a system.

Answer 2

Given that both the assertion and the reason are correct and logically connected

The statement is "True."

This is a true statement, and we can break down the assertion and reason to understand why:

Assertion: The potential difference between any two points in an electric field depends only on initial and final position.

Reason: Electric field is a conservative field, so the work done per unit positive charge does not depend on the path followed.

Step-by-step explanation:

1. Potential Difference in an Electric Field:

- The potential difference (also known as voltage) between two points in an electric field is a measure of the electrical potential energy difference between those points.

- It is defined as the work done per unit positive charge when moving a charge from one point to another in the electric field.

2. Conservative Field:

- An electric field is considered a conservative field. In a conservative field, the work done by or against the field when moving an object (in this case, a positive charge) from one point to another does not depend on the specific path taken.

3. Path Independence:

- In a conservative field like the electric field, the potential difference between two points depends solely on the initial and final positions of the charge, not on the path taken.

- This means that if you move a positive charge from point A to point B in an electric field, the potential difference (voltage) between these points will be the same regardless of the path you choose to follow.

4. Work Done per Unit Positive Charge:

- The reason given in the statement correctly relates to the work done per unit positive charge (which is the definition of potential difference or voltage).

- In a conservative field like the electric field, the work done per unit positive charge (or voltage) is path-independent.

The potential difference between any two points in an electric field depends only on the initial and final position due to the conservative nature of the field, where the work done per unit positive charge does not depend on the path followed.