Finding energy in a 4 object charge system

AI Thread Summary
The discussion revolves around calculating the potential energy in a four-object charge system, specifically when moving a charge of +2.0×10−5 C from position C to D. Participants highlight the importance of including all charge pairs in the calculations, particularly the interaction between q1 and q3, which was initially overlooked. The user initially calculated the total energy as 126 J but was informed that the correct answer should be -105 J, indicating errors in sign and numerical values. Further clarification is requested on the calculations, emphasizing the need to account for the signs of the charges in the potential energy equations. Accurate calculations are essential for determining the correct potential energy in such systems.
Anthony Santelices
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Homework Statement


An object with charge +2.0×10−5 C is moved from position C to position D in the figure (Figure 1) . q1 = q3 = +10.0×10−5 C and q2 = −20.0×10−5 C. All four charged objects are the system.

Here's a picture to the problem
upload_2016-3-28_18-27-18.png

Homework Equations


$$ F = \frac {kq_1 q_2}{r^2} $$
$$ U_e = \frac {kq_1 q_2}{r} $$
$$ a^2+b^2=c^2 $$

The Attempt at a Solution


I first attempted finding all the energy for the system by finding the initial potential electric energy for each pair of charged objects and added them together. I managed to find the distance from ## q_2 ## to ## q_1## and ##q_3## using Pythagorean theorem.$$ c → q_1, c → q_2, c → q_3, q_2 → q_1, q_2 → q_3 $$
Unfortunately after putting the added energies it came up as wrong.
 
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Hello Anthony, :welcome:

I suspect something went wrong with your calculations, can you show them, please ?
Note that 'the system' consists of four charges!
 
This is the picture :

upload_2016-3-29_0-26-6.png

Anthony Santelices said:

Homework Statement


An object with charge +2.0×10−5 C is moved from position C to position D in the figure (Figure 1) . q1 = q3 = +10.0×10−5 C and q2 = −20.0×10−5 C. All four charged objects are the system.

Here's a picture to the problem

Homework Equations


$$ F = \frac {kq_1 q_2}{r^2} $$
$$ U_e = \frac {kq_1 q_2}{r} $$
$$ a^2+b^2=c^2 $$

The Attempt at a Solution


I first attempted finding all the energy for the system by finding the initial potential electric energy for each pair of charged objects and added them together. I managed to find the distance from ## q_2 ## to ## q_1## and ##q_3## using Pythagorean theorem.$$ c → q_1, c → q_2, c → q_3, q_2 → q_1, q_2 → q_3 $$
Unfortunately after putting the added energies it came up as wrong.
Have you left out the pair q1-q3?
 
ehild said:
This is the picture :

View attachment 98121

Have you left out the pair q1-q3?
Ah yes! It appears I did. However, even without having it I was getting 126 J. It says that the answer is -105 J. So that tells me I messed up somewhere while calculating with all the ##U_e##'s.
BvU said:
Hello Anthony, :welcome:

I suspect something went wrong with your calculations, can you show them, please ?
Note that 'the system' consists of four charges!
I don't have access to my work atm as I am not home. I will make sure to post it as soon I get the chance!
 
BvU said:
Hello Anthony, :welcome:

I suspect something went wrong with your calculations, can you show them, please ?
Note that 'the system' consists of four charges!
These are the numbers I got along with the added ##q_1, q_3##
$$ U_{c,q1} = \frac {(9*10^9)(+2.0*10^{-5}) (+10.0*10^{-5})} {2.0} = 9\ J$$
$$ U_{c,q2} = \frac {(9*10^9)(+2.0*10^{-5}) (-20.0*10^{-5})} {2.0} = 18\ J$$
$$ U_{c,q3} = \frac {(9*10^9)(+2.0*10^{-5}) (+10.0*10^{-5})} {2.0} = 9\ J$$
$$ U_{q2,q1} = \frac {(9*10^9)(-20.0*10^{-5}) (+10.0*10^{-5})} {2\sqrt2} = 45\ J$$
$$ U_{q2,q3} = \frac {(9*10^9)(-20.0*10^{-5}) (+10.0*10^{-5})} {2\sqrt2} = 45\ J$$
$$ U_{q1,q3} = \frac {(9*10^9)(+10.0*10^{-5}) (+10.0*10^{-5})} {4.0} = 22.5\ J$$
 
You ignored all the negative signs.
 
ehild said:
You ignored all the negative signs.
I've tried it with the negative signs, but I end up getting -68. The correct answer shown was -105, so I don't know exactly where I went wrong.
 
You must include the signs of the charges,
And even the numerical values of U(q2,q1) and U(q2,q3) are wrong.
 
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