When do I use a particular equation for electric potential energy?

[PsxDcSquall]

Hey I know this question has been asked before but none of the other threads seem to really shed some clarity on the issue.

I have been working through the Kaplan High Yield problem solving guide (which I really like BTW). In the problems dealing with electrostatics the first problem says to use deltaU=qdeltaV for the change in electric potential energy.

However when we get to the third worked problem it says to solve for potential energy by using U=kq1q1/r. In its explanation it says

"Potential energy can only be defined as a relative value, but in these types of problems, it is easiest to use the definition that the potential energy is zero at infinite distance. This way you can use the formula U=kq1q2/r, which saves time as compared to using deltaU=qdeltaV by bypassing the step of first calculating V."

Basically, I don't understand the criteria behind when to use which equation and how using the definition of potential energy being zero at infinite distance allows you to use a particular equation.

Thanks for helping me!!!

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[ballofnerves]

They are actually the same equation! The potential V can be defined as:

V=k q1/r

This is the potential energy that a charge of one coulomb would possess at a distance r from a charge q1. So if you want to figure out the potential energy of an arbitrary charge q2, you need to multiply V by the quantity of charge q2:

U = q2 V = q2 (k q1)/r = k q1 q2 / r

The theory behind the zero potential at infinity is not too important. Just try to imagine the force that a small charge would feel at an infinite distance from another charge. It would obviously be very small. It turns out that using infinity as this reference point allows the derivation of these equations, but I would not consider it too important for the MCAT.

 

[futuredoctor10]

Yeah ballofnerves' explanation is a great way to derive the 2nd expression.

Basically, I don't understand the criteria behind when to use which equation and how using the definition of potential energy being zero at infinite distance allows you to use a particular equation.

For the MCAT, I think just look at what they're asking you to find.

If they want the electric potential energy: PE(elec) = qV

If they want the Potential Energy of a system of 2 charges: PE = kqq/r

Not trying to make this overly simplistic, but I think for the MCAT chances are they will explicitly tell you what they want- if they want PE of the system and provide 2 charges use the 2nd equation. If they want the electric PE (defined as work needed to move the charge from infinity to its current location), then use the 1st equation.

Hope this helps!

 

[PsxDcSquall]

Thanks a lot that makes things a lot clearer!