Electrical Potential Energy problem

In summary: So, in summary, the problem involves finding the electrical potential energy of a pair of point charges, one held fixed at the origin and the other placed on the x-axis at a distance of 0.250m from the origin. The formula used is U = (1/4*pi*Eo)*(q1*q2/r), and the only mistake in the work shown is the extra negative sign in the potential energy formula. This is because the electrical potential energy formula does not have an additional negative sign like the gravitational potential energy formula does. The incorrect answer may have been due to a mistake with the units, but was ultimately resolved by correcting the value for micro to be ^-6 instead of ^-9.
  • #1
sirdeity
2
0
Hello. I'm just stuck on a problem. A point charge Q=+4.60x10^(-9)C is held fixed at the origin. A second point charge q=+1.20x10^(-9)C with mass of 2.80x10^(-4)kg is placed on the x-axis, 0.250m from the origin.

The problem asks, "What is the electrical potential energy U of the pair of charges?"

Okay, so I tried using the formulas:
-(Ub-Ua)=-deltaU and U=((1)/(4*pi*Eo))*((q1*qo)/(r))

Where I'm confused is that q1 and qo appear the same in both Ua and Ub, thus wouldn't Ub-Ua cancel and equal zero? Here's my obviously incorrect work:

-(((1)/(4*pi*Epsilono))*(((1.2x10^(-9))(4.6x10^(-9)))/(.25m)) = -1.98x10^(-7)

However, the correct answer according to the back of the book is "0.198J." Can anyone with patience please explain what I'm doing wrong? This material is new to me. I'm in a 5 week summer calculus 2 based engineering physics 2 course (PHY 122). We only just started talking about this material yesterday.
 
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  • #2
You do not need the delta U equation. That formula applies when you change from one situation at one potential energy, to another situation with another potential energy.

Here you do not have a change in potential energy. The potential energy is staying the same, and they want you to find what it is. So, the only relationship you'll need is:

[tex] U = \frac{1}{4\pi\epsilon_o}\frac{q_1q_2}{r}[/tex]

I am getting the same answer you are, but positive. Your extra negative sign comes in because you have a negative sign because that negative sign you have in the potential energy formula shouldn't be there. Unlike the gravitational potential energy expression, the electrical potential energy expression does not have that extra negative sign. Just make sure if the charges are negative, you use put their negative signs in the "U" formula!

Other than that, I think your work is correct. You are off by seven factors of ten. I think you may want to check to make sure that you are actually using the correct units, just in case you misread them. Also, if check your unit conversions if you did any. Then, if that isn't it, check the accuracy of the books answer with someone else like your professor.
 
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  • #3
Thank you very much for your help. I actually figured out the problem last night, after about 3 hours of trying various things. The thing that was messing me up was that I assumed micro was ^-9 when it is actually ^-6.

It was a silly mistake on my part. Thanks again.
 
  • #4
sirdeity said:
Thank you very much for your help. I actually figured out the problem last night, after about 3 hours of trying various things. The thing that was messing me up was that I assumed micro was ^-9 when it is actually ^-6.

It was a silly mistake on my part. Thanks again.

No problem. I'm glad you figured it out!
 

FAQ: Electrical Potential Energy problem

What is electrical potential energy?

Electrical potential energy is the energy that is stored within an electric field due to the position of charged particles. It is the potential for work to be done by the electric field on a charged particle.

How is electrical potential energy calculated?

The formula for calculating electrical potential energy is U = qV, where U is the potential energy, q is the charge of the particle, and V is the electric potential at the location of the particle.

What factors affect electrical potential energy?

The factors that affect electrical potential energy are the amount of charge present, the distance between the charged particles, and the strength of the electric field.

What is the unit of measurement for electrical potential energy?

The unit of measurement for electrical potential energy is the joule (J). In some cases, the electron volt (eV) may also be used.

How is electrical potential energy related to electric potential?

Electrical potential energy is directly related to electric potential, as electric potential is defined as the potential energy per unit charge. This means that the higher the electric potential, the greater the electrical potential energy of a charged particle in that field.

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