Why is work done by a nonconservative force negative

[x86]

In my textbook it says that work done by a nonconservative force (an applied force) has the same sign as the change of potential energy?

For instance, if I push a positive test charge from an infinite distance away to a negative charge, then the test charge goes from high potential energy to low potential energy. Why is the work that I am doing on it negative? Shouldn't the work I'm doing on it be positive, because I'm losing energy trying to push the test charge?

 

[Chestermiller]

You are not pushing the positive charge toward the negative charge. You are trying to hold it back. So the force you are exerting is in the opposite direction from the direction that the charge is moving.

Chet

 

[nasu]

Are you sure this is the exact formulation in your book?
A non-conservative force does not have a potential energy associated with it. So in general you can have a non-conservative force and no potential energy to speak of. Why would the work of this non-conservative be the negative of a non-existent potential energy?

If you have both conservative and non-conservative forces, the work of the conservative force is (by definition) the negative of the change in PE associated with this conservative force. The work of the non-conservative is whatever the formula for work provides, for that force.