Finding the distance of 2 charges

[kamehamehaaa]

Homework Statement

On attachment called Part B

Homework Equations

To get part A, I used a formula that I derived to be:

square root [(2kq^2)/rm)] = v

where
q =2.6 *10^-6 C
k = 8.99*10^9 (Nm^2)/C^2
r = 1.27m
m = .0028 kg

The Attempt at a Solution

Now for part B it says to calculate the distance r when it is half of v, so I thought maybe I could rearrange the equation above to

(2kq^2)/((v^2)*m) = r

so it would look like...

[2 * 8.99^9 * (2.6*10^-6)^2]/[((5.84/2)^2)*.0028] = r

I used dimensional analysis and it comes out to be

[(Nm^2/C^2)C^2]/[(kgm^2)/(s^2)]

then I cancel what I can to get

(Ns^2)/kg which in turn, becomes

1ms^2/s^2 which at the end turns out to be left with only meters...

So it seems like I'm right but obviously I am not...

OK in the attachment are the answers I submit after doing so many bizaarrreee calculations... ANy help would be appreciated... I think the reason I'm not getting hte correct answer is becuase the question states "at infinity" and I have no Idea what that means...

 

[anathema]

Thank you for sharing your attempted solution for part B of the problem. It looks like you have correctly rearranged the equation to solve for r. However, there are a couple of things to keep in mind.

Firstly, when solving for r, you want to use the half of v value, which in this case would be 5.84 m/s, not 5.84/2 m/s. So your final equation should look like:

[2 * 8.99^9 * (2.6*10^-6)^2]/[(5.84)^2*.0028] = r

Secondly, the "at infinity" in this problem means that the two charges are so far apart that the force between them can be considered negligible. In other words, the distance between them is so large that it essentially becomes infinite. So when solving for r, you are finding the distance between the two charges when the force between them is essentially zero.

I hope this helps clarify things for you. Keep up the good work in deriving and solving equations!

 

[Moetasim]

I can provide a response to your attempt at solving this problem. Your approach of rearranging the equation to solve for r is correct. However, the reason you are not getting the correct answer is because your conversion from units is incorrect.

When using dimensional analysis, it is important to keep track of the units and their corresponding powers. In your calculation, you have the unit of Coulomb squared in the numerator and in the denominator, which cancels out leaving you with just meters. This is not correct.

To solve this problem, you need to use the correct conversion factors for each unit. For example, for Newtons, you need to use the conversion factor of 1 N = 1 kg*m/s^2. Similarly, for Coulombs, you need to use the conversion factor of 1 C = 1 A*s. By using the correct conversion factors, you will end up with the correct units and the correct answer.

Additionally, the term "at infinity" means that the distance between the two charges is extremely large, approaching an infinite distance. This can be represented by using a very large number, such as 10^9 or 10^12, for the distance r. This will also affect your final answer.

In conclusion, your approach to solving this problem is correct, but you need to use the correct conversion factors and consider the distance as approaching infinity to get the correct answer. I hope this helps and good luck with your calculations.