Potential Energy of Opposite Charges: Impact of Distance Change

[chemistry4all]

Homework Statement

Two oppositely charged balls are hung by strings from a wooden dowel. The two balls are separated by a distance of R.

a) If the balls are moved along the dowel until their separation is 3/2 R, has their potential energy increased or decreased?

b) What is the magnitude (size) of the effect on the potential energy (by what factor does it change)?

Homework Equations

Nothing is given but the 3/2 R and I am not sure which equation or equations to use. I am aware of PE= mxgxh and that's about it.

The Attempt at a Solution

 

[vela]

You've given the expression for gravitational potential energy, but this problem involves electric potential energy because the balls are interacting via the electric force. You need to look up the expression for the electric potential energy between two point charges.

 

[chemistry4all]

Here is what I have found from my textbook and was not sure exactly how to use it.


The formula for electrostatic potential energy is Eel=kQ1Q2/d

Eel = total electrostatic energy
k= 8.99x10^9 J-m/c^2
Q1= would be charge of +1
Q2= would be charge of -1

Then I plugged it all in Eel=(8.99x10^9)(+1)(-1)/(3/2)
Eel= -5.9933333x10^9 and is this answer in J-m/c^2 units. I am confused on the dimensional analysis. I am very good at it but d has R is that the units and Q1 and Q2 what would be the units so I can cancel them out and get the correct units?

Also is this correct so far. I am still not sure?

 

[vela]

The problem is asking you to compare the electric potential energy between two cases. It doesn't give you numbers, though, so you can't work out a specific amount of energy for each case. Your expressions will be in terms of q, the magnitude of the charge on each ball, and R, the initial distance between them.

The balls are oppositely charged, so if one ball has charge q, the other has charge -q. The distance between them initially is R, so the potential energy U (it's best to avoid the letter E since that's usually used to stand for the electric field) is

$$U_i = \frac{kq(-q)}{R} = -\frac{kq^2}{R}$$

Now when the distance between them increases to 3/2 R, the potential energy is now

$$U_f = \frac{kq(-q)}{3R/2} = -\frac{2}{3} \frac{kq^2}{R}$$

So now you want to figure out for part (a), is U_i>U_f or U_i<U_f. Note that you don't need to know specific values for q and R because both U_i and U_f are proportional to the same quantity, but you should consider whether the potential energies are positive or negative because it'll affect your answer.

Once you think you have an answer, you should consider whether it's reasonable or not. The balls are oppositely charged, so they're attracted to each other. Would you have to do additional work to separate them? Does that jibe with how you think the potential energy changes?

 

[chemistry4all]

okay chrages are measured in C which is coloumbs now i have the correct units.


The charges are not -1 and +1 they are proton=(1.6x10^-19)
electron=(-1.6x10^-19)

R which is d was 3/2

k=8.99x10^9

so I used the same formula Eel=kQ1Q2/(3/2)


Eel=(8.99x10^9 J-m/c^2)(1.6x10-19 C)(-1.6x10-19)/(3/2)

Eel=-1.5342933333x10^-28 J-m


Am I correct now. I am still not sure how to figure out the answers tot he questions about magnitude and if its increases or decreases in potential energy. Please can someone help.

 

[chemistry4all]

I understand the formula and how its used but I don't know how to still get the magnitutde and determine the right answers. I am not understanding something.

I have been on this damn one question for 6 hrs I am done I give up. Thanks for everyones help.

 

[vela]

You seem to have this obsession with requiring numbers. When it says the final separation is 3/2 R, it doesn't mean that R=3/2. It means the final distance was 3/2 times the original distance, which was R. You don't know what the actual value of R is, but you don't need to.

Same with the charges. All the problem says is the balls have opposite charges, so one has a charge of +q and the other has -q. You don't know what the actual value of q is, but, again, it doesn't matter.

The point of the problem is to understand how the potential energy depends on separation, to be able to answer questions like: If you increase the separation, does it go up or down? How does it vary -- proportionally, inverse proportionally, as 1/r^2?