Find potential energy of system with 3 charges

[mbmcgee]

Homework Statement

Three charges are at rest on the z-axis, q1 = 2 mC at z = 0 m, q2 = 0.6 mC at z = 1 m, and q3 = -1.5 mC at z = -0.4 m. What is the potential energy of this system?

Homework Equations

The Attempt at a Solution

Here is what i tried: K( (q1*q2)/r + (q1*q3)/r + (q2*q3)/r )

note: r is the distance between the two charges

Is this the right equation to use, and I just make a mathematical error?
If not, any suggestions on what to do?

-michael

 

[alphysicist]

Hi michael,

Homework Statement

Three charges are at rest on the z-axis, q1 = 2 mC at z = 0 m, q2 = 0.6 mC at z = 1 m, and q3 = -1.5 mC at z = -0.4 m. What is the potential energy of this system?

Homework Equations

The Attempt at a Solution

Here is what i tried: K( (q1*q2)/r + (q1*q3)/r + (q2*q3)/r )

note: r is the distance between the two charges

Is this the right equation to use, and I just make a mathematical error?
If not, any suggestions on what to do?

-michael

Your equation looks right to me; what numbers did you use in the equation, and what answer did you get?

 

[mbmcgee]

alphysicist:
thanks for the reply

i got: K( (1.2E-12)/1 + (3E-12)/.4 + (9E-13)/1.4 )
which i ended up with 83,973.6 J somethings wrong lol

 

[alphysicist]

alphysicist:
thanks for the reply

i got: K( (1.2E-6)/1 + (3E-6)/.4 + (9E-7)/1.4 )
which i ended up with 83,973.6 J somethings wrong lol

I believe you did not take into account that q3 is negative.

 

[mbmcgee]

I believe you did not take into account that q3 is negative.

Ok, I reworked the problem with mC this time and took into account the -q3 but still get the wrong answer. I thought you were supposed to take the magnitude of the charges so I worked it that way but get a different but wrong answer.

edit: I edited the mC in my second post to be correct. I did not edit the answer.

 

[alphysicist]

Ok, I reworked the problem with mC this time and took into account the -q3 but still get the wrong answer. I thought you were supposed to take the magnitude of the charges so I worked it that way but get a different but wrong answer.

edit: I edited the mC in my second post to be correct. I did not edit the answer.

So these are in microCoulombs and not milliCoulombs? If it is microCoulombs (and you don't want to use the symbol for micro) then it's better to write it as 2uC, for example, rather than 2mC.

What did you get for the answer?

(By the way, about using magnitudes: when calculating forces or fields with Coulomb's law you often only want to calculate the magnitude, because you can often get the direction from a force diagram. But for potential and potential energy calculations you keep the sign of the charges.)

 

[mbmcgee]

So these are in microCoulombs and not milliCoulombs? If it is microCoulombs (and you don't want to use the symbol for micro) then it's better to write it as 2uC, for example, rather than 2mC.

What did you get for the answer?

(By the way, about using magnitudes: when calculating forces or fields with Coulomb's law you often only want to calculate the magnitude, because you can often get the direction from a force diagram. But for potential and potential energy calculations you keep the sign of the charges.)

Nevermind I am an idiot. It is milliCoulombs not micro. So once i took -q3 into account like you said i got the right answer which is -62402.4J. Thanks for the help.

My brain does not work to well so late at night :)

 

[alphysicist]

Nevermind I am an idiot. It is milliCoulombs not micro. So once i took -q3 into account like you said i got the right answer which is -62402.4J. Thanks for the help.

My brain does not work to well so late at night :)

Glad to help! (And believe me I understand about those late nights and what they can do to your thinking.)