# Electric Potential Energy of A System of Point Charges

• Oaksmack
In summary, a particle of charge q=7.5x10^-6 Coulombs is released from rest at .6m on the x axis, and moves due to a charge Q = -20x10^-6 C at the origin. Using the equation KE1 + U1 = KE2 + U2, with KE1 and U1 being 0, we can solve for the kinetic energy of the particle after it has moved .4 meters. However, in the calculation, one of the potential energies should be multiplied by 1/2, as the charges are opposite in sign. This results in a kinetic energy of 4.5 J, which is different from the answer given in the book.
Oaksmack
A Particle of charge q=7.5x10^-6 Coulombs is released from rest at .6m on the x axis. The particle moves due to charge Q = -20x10-6 C. What is the Kinetic Energy of the particle the instant it has moved .4 meters if Q stays fixed at the origin?

Here I used KE1 + U1 = KE2 + U2
Which equals 0 + (kqQ)/.6 = KE2 + kqQ/.2
I got 2.2475 = KE2 - 6.7425
so KE2 = 8.99 or 9 Joules.
The answer is 4.5 J in the book however.

Where did I go wrong? My answer for the first part of the question, with Q =positive 20 micro Coulombs, was correct. Is the KE for attraction supposed to be multiplied by 1/2 as opposed to repulsion? Please help!

My k value by the way is correct, at 8.99x10^9.

both potential energies should have the same sign. In your equation, one of them is positive the other is negative.

## 1. What is electric potential energy?

Electric potential energy is the energy that an object possesses due to its position in an electric field. It is the potential for work to be done on the object by the electric field.

## 2. How is electric potential energy calculated?

The electric potential energy of a system of point charges is calculated using the formula U = kQq/r, where k is the Coulomb's constant, Q and q are the magnitudes of the charges, and r is the distance between them.

## 3. Can the electric potential energy of a system of point charges be negative?

Yes, the electric potential energy of a system of point charges can be negative if the charges have opposite signs. This indicates that work must be done to bring the charges closer together.

## 4. How does the distance between point charges affect the electric potential energy of a system?

The electric potential energy of a system of point charges decreases as the distance between the charges increases. This is because the electric force between the charges decreases with distance, resulting in a lower potential energy.

## 5. Can the electric potential energy of a system of point charges change?

Yes, the electric potential energy of a system of point charges can change if the positions of the charges change. This change in potential energy can be calculated using the same formula, U = kQq/r, as the distance between the charges changes.

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