Find potential energy of system with 3 charges

In summary, the problem involves three charges at rest on the z-axis with values of 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. The potential energy of this system is calculated using the equation K( (q1*q2)/r + (q1*q3)/r + (q2*q3)/r ), where r is the distance between the two charges. It is important to take into account the sign of the charges in the calculation. The correct answer is -62402.4J.
  • #1
mbmcgee
7
0

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
 
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  • #2
Hi michael,

mbmcgee said:

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?
 
  • #3
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
 
Last edited:
  • #4
mbmcgee said:
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.
 
  • #5
alphysicist said:
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.
 
  • #6
mbmcgee said:
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.)
 
  • #7
alphysicist said:
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 :)
 
  • #8
mbmcgee said:
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.)
 

1. What is potential energy?

Potential energy is the energy that a system possesses due to the position or configuration of its components. It is stored energy that can be released and converted into other forms, such as kinetic energy.

2. How is potential energy related to electric charges?

In a system with electric charges, potential energy is the energy associated with the interaction between the charges. The potential energy is directly proportional to the magnitude of the charges and inversely proportional to the distance between them.

3. Can the potential energy of a system with 3 charges be negative?

Yes, the potential energy of a system with 3 charges can be negative. If the 3 charges have the same sign (positive or negative), their potential energy will be positive. However, if 2 of the charges have opposite signs, their interaction will result in a negative potential energy.

4. What is the formula for calculating the potential energy of a system with 3 charges?

The formula for calculating the potential energy of a system with 3 charges is U = k(q1q2/r12 + q1q3/r13 + q2q3/r23), where U is the potential energy, k is the Coulomb constant (9 x 10^9 Nm^2/C^2), q1, q2, and q3 are the charges, and r12, r13, and r23 are the distances between the charges.

5. How can the potential energy of a system with 3 charges be changed?

The potential energy of a system with 3 charges can be changed by altering the positions of the charges or by changing the magnitude of the charges. The potential energy will increase as the charges move closer together and decrease as they move farther apart. Additionally, increasing the magnitude of the charges will also increase the potential energy of the system.

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