A charge is moved from one point to another in an electric field. Explain briefly the relationship between electric potential difference and work done in moving this charge.
The relationship between electric potential difference (V) and work done (W) while moving a charge is explained by the equation:
W = qV
where q represents the charge being moved.
To understand this relationship, let's break it down step by step:
1. Electric Potential Difference (V):
Electric potential difference, also known as voltage, measures the difference in electric potential between two points in an electric field. It represents the work done per unit charge (W/q) to move a charge from one point to another.
2. Work Done (W):
Work done in physics is defined as the product of the force applied on an object and the distance it moves in the direction of the force. In the case of moving a charge in an electric field, the force acting on the charge is the electrostatic force, given by F = qE, where E is the electric field strength. Therefore, the work done to move the charge is given by W = F*d, where d is the displacement of the charge.
Now, let's combine these two concepts:
The electrostatic force acting on a charge is parallel to the displacement of the charge, making it a conservative force. This means that the work done in moving the charge between two points in an electric field only depends on the positions of those points and not on the path taken.
The work done on a charge is given by the product of the force acting on the charge and the distance it moves. In terms of electric potential difference, we can rewrite the electrostatic force formula as F = qE = q(V/d), where E = V/d.
Substituting this into the equation for work, we get:
W = q(V/d)*d = qV
Therefore, the work done (W) in moving a charge (q) between two points in an electric field is equal to the charge multiplied by the electric potential difference (V) between those points.