Work done by Electric Field vs work done by outside force I'm confused as to the signage of the equation:
W=qv, W=-U, W=-qv?
When is work positive? When is it negative? Why is this different for the work done by the electric field vs the work done by an outside force?
What is the relationship between electric potential energy and work?
 A: Work is positive when the projection of the force vector onto the displacement vector points in the same direction as the displacement vector(you can understand negative work in a similar way). 
Let's call the charge that you are trying to move Q. Observe that if you want to calculate the work done by the electric field on this charge, you simply invoke $W_{electric field} = Q \cdot \int_{R_1}^{R_2} \vec{E} \cdot d \vec{r} $  (this follows immediately from definition of electric force)
Now, recall that the definition of electric potential in the simple case of a radial electric field is $$ \Delta V = - \int_{R_1}^{R_2} \vec{E} \cdot d \vec{r} $$
The negative sign here is the KEY! 
These definitions imply that if you begin with a stationary charge Q at $R_1$, move it to $R_2$ and fix its position, then $$W_{net} = 0 $$ $$W_{electric field} = - Q \Delta V$$ $$W_{outside} = Q \Delta V$$ 
Therefore you have to be really careful with definitions here. Always keep in mind what separate forces are doing work.
