Potential Energy of a pair of charges question

[fisixC]

Homework Statement

Two point charges of magnitude 4.79 nC and
−1.11 nC are separated by 39.4 cm.
The acceleration of gravity is 9.8 m/s^2
The Coulomb constant is 8.98755×10^9
N · m^2 /C^2.

What is the potential energy of the pair of
charges?
Answer in units of V.

Homework Equations

Voltage = Potential energy / charge
Voltage = (k*q)/(r)

r being the distance
k being Coulomb's constant
and q being the charge of the point charge

Coulomb's constant: 8.98755E9

The Attempt at a Solution

So I think the problem wants me to find the voltage of the system judging by the "Answer in units of V. So I solved each charge for the voltage then added them together:

Vq1 = (k * 4.79e-9) / (39.4/100) = 109.264884518V
Vq2 = (k * 1.11e-9) / (39.4/100) = 25.3202550761V

So the sum of the two (Vq1 + Vq2) would be the total potential energy of the pair of charges in unit V which equals: 134.585139594V, which is wrong.

I believe I may be reading the question wrong possibly, or just using the wrong method.

 

[fisixC]

Help anyone?

 

[fisixC]

At all. D:

 

[fisixC]

Help still appreciated.

 

[Matterwave]

It actually makes no sense to express the potential energy in terms of volts. Volts is energy/charge and therefore is not a measure of energy itself.

However, to do this, you should know exactly that the equation V=kq/r means. In that equation, the q is the charge of the SOURCE charge, and so you need to define which charge is your source charge, and which charge is your test charge (arbitrary). And then U=q(test)*V which you will find is actually just kq1q2/r! But kq1q2/r is in units of Joules, and not volts, so I'm pretty sure there's something wrong with the wording of the question.

 

[fisixC]

If we assume the question means the electric potential energy of the pair of charges is it possible then?

 

[Matterwave]

Electric potential energy is still an energy, and is expressed in Joules...in fact that is exactly U.

The question would make sense if it asked you to answer in terms of eV (electron volts).

 

[fisixC]

Can you help me assuming the question said to find the "electric potential" of the pair of charges?

 

[Matterwave]

Can you just type out the exact wording of the problem? Are you sure you typed it out right in your first post?

 

[fisixC]

Yes I am entirely certain I typed it out correctly it does say "Answer in units of V" in the original problem. This should be able to be solved if we assume it's electric potential, since that is what we are studying in class.

 

[SammyS]

The Potential Energy of the system may be obtained from either of the following:

$$U=q_2\cdot V_{q_1}}\quad\text{ or }\quad U=q_1\cdot V_{q_2}}$$

In either case you could express the answer in units Volt-Coulombs.

 

[fisixC]

Are you saying that I should just solve for potential energy?

 

[Matterwave]

Sammy is right, but note that 1Volt-Coulomb=1Joule. His answer is exactly the same as mine.

 

[fisixC]

This is going to get me a ridiculously small answer.

u = k(4.79e-9)/(39.4/100) * 1.11e-9 = 1.21284e-7

Do I need to respect that the q2 is negative so my potential energy will be negative?

 

[fisixC]

This is going to get me a ridiculously small answer.

u = k(4.79e-9)/(39.4/100) * 1.11e-9 = 1.21284e-7

Do I need to respect that the q2 is negative so my potential energy will be negative?

Solved: It is negative because the other charge is negative and there was a typo because I answered in Joules instead of Voltage and I still got the right answers which is what is quoted above but negative: -1.21284e-7 J