Electrostatics - Work done by an electron

[milkyway11]

The problem states: how much work is done in moving an electron from a distance of 1nm to a distance of 10nm away from a hydrogen nucleus?

My attempt at the problem is using the W=\DeltaU=q\DeltaV. With this equation I would get a positive work. However, when I reason through the question, I would expect that it would have a negative work because I always thought the charges have more potential U when they are close to each other.

Could it be that the positive work is due to the unlike charges attract more at near distance and it takes more work to compensate the attractive force in order to separate them?

Thanks!

 

[gneill]

Consider a case where you're moving the electron in a straight line from a distance of 1nm to a distance of 10nm along the x-axis. Since the particles are attracting each other, you have to apply a force in the +x direction to do this. The distance that you move the electron is also in the +x direction. Since work is force dot distance (vector dot product), the work done by the force must be positive.