Question

A point charge with charge q1 is held stationary at the origin. A second point charge with charge q2 moves from the point (x1, 0) to the point (x2, y2). Please use k for Coulomb's constant rather than writing it out as (1/4πϵ0).

How much work W is done by the electrostatic force on the moving point charge? Express your answer in Joules and use k for Coulomb's constant.

Answer 1

here q1 at (0,0) and q2 at (x2, y2) the distance (r) between the charges is
r = √((x2-0)² + (y2-0)²) = √(x2² + y2²).
If this is not clear, make up values for x2 and y2 and draw a diagram. R is the hypotenuse of a right-angled triangle.

Final potential energy is E2 = kq1q2/r = kq1q2/√(x2² + y2²)

The change in potential energy is E2 – E1.

The question is ambiguous. If some external force does the work, then W = E2 – E1.

But if it is the *internal* force doing the work, then
W = E1 – E2. If this is not clear, think about the work done by an object’s weight when the object freely falls. The object descends so its potential energy decreases so the change in potential energy is negative, but the displacement and force are in the same direction so the work done by the weight is positive.