For potential energy problems, is it enough to state the potential energy at infinity? I've seen two different ways of stating the potential energy of an object (specifically for electric potential).
For some problems, I've seen it defined as at $d = 0$, $PE_{object} = 0$. When you lift an object up, you increase its potential energy.
In other problems, I've seen it defined as at $d = \infty$, $PE_{object} = 0$. In this case, how would I find the potential energy at some finite point in the field?
I understand this is probably a basic concept, but I'd appreciate some help understanding it.
 A: These two different ways are actually equivalent.
Let's consider a situation when there is an electric field of some charge $Q$ and we choose infinity as a zero level of potential field. In this case the formula of potential energy of some other charge $q$ in this potential field is: $$E = k * \frac{Q * q}{r}$$
I guess this answers your question - this is the formula which gives you the potential energy.
But you can choose any point as zero level of potential energy! For example you can choose that potential energy is zero at some distance $r_0$ from the $Q$ charge. The formula for potential energy at some distance $r$ will be a little more complicated: $$E = k * \frac{Q * q}{r} - k * \frac{Q * q}{r_0}$$
You can even choose to define potential energy as $$E = k * \frac{Q * q}{r} - C$$ and choose any $C$ - even such that potential energy is not zero anywhere!
But whatever formula you choose, when you "lift" your body (that is increase the distance between $Q$ and $q$ from $r$ to $r+dr$) the difference of potential energy would be the same! In our case if both $Q$ and $q$ are positive the energy will decrease. If you need to calculate how the speed of the body would change, or how much gasoline you need to move the bodies - the answers would be the same whatever formula you choose. Because only the potential energy difference matters. You only need to decide which one of the formulas you will use and use the chosen one for all the calculations.
But which one do you need to choose? First one looks like most simple. But for some problems it can be more convenient to choose other versions. It depends on the problem you need to solve.
