Why can't i calculate this system of electric potential?

[mr_coffee]

Hello everyone, I'm having troubles figuring out why this problem is wrong. In the quark model of fundamental particles, a proton is composed of three quarks: two "up" quarks, each having charge +2e/3, and one "down" quark, having charge -e/3. Suppose that the three quarks are equidistant from one another. Take the distance to be 1.32 10-15 m.

(a) Calculate the electric potential energy of the system of only the two "up" quarks.
wrong check mark eV
(b) Repeat for all three quarks.
eV

for (a) I used the following i found in the boook:
The electric potential enegery of a system of fixed point charges is equal to the work that must be done by an external agent to assemble the sytem, bringing each chage in from an infintie distance.

U = W = q2V = (1/4Pi*Eo)((q1*q2)/r);
U = (1/4Pi*Eo)(2/3)^2/(1.32e-15m) = 3.03E24 eV which is wrong, what did i mess up? Thanks.

 

[anathema]

Hi there, thank you for sharing your question with us. After looking at your calculations, I believe you may have made a mistake in your unit conversion. The formula you have used for electric potential energy is correct, but the unit for electric potential energy is typically expressed in Joules (J) rather than electron volts (eV). So, your answer of 3.03E24 eV should actually be 3.03E-9 J. I hope this helps and good luck with your calculations!

 

[quicknote]

I can tell you that the reason why you are not able to calculate the electric potential of this system is because you are using the wrong formula. The formula you used is for calculating the electric potential energy between two point charges, but in this case, you have three charges that are equidistant from each other.

To calculate the electric potential energy of a system of point charges, you need to use the formula: U = (1/4πε0)∑(qi*qj)/rij, where ∑ represents the sum of all possible combinations of charges, qi and qj are the charges of the particles, and rij is the distance between them.

Applying this formula to your problem, for (a), you will have two terms in the summation, one for the interaction between the two "up" quarks and one for the self-energy of each "up" quark. For (b), you will have three terms in the summation, accounting for the interaction between all three quarks and their self-energies.

I hope this helps you understand why your calculations were incorrect. It is important to use the correct formula for the specific system you are trying to calculate.