# Potential Energy of a System of charged particles

• sniper_spike
In summary, you are trying to figure out the voltage between two points by summing the voltages between those points and taking the maximum.
sniper_spike

V = kQ/r
PE = Vq

## The Attempt at a Solution

Tried a lot of ways... get an order of magnitude less than the answer and also off by a bit too.

Please help. I think you are supposed to take V at each location then multiply by q since this is PE. I carry everything in vector form but my numbers are confusing. Attraction is supposed to be negative PE. Well we have attraction/ repulsion both working on a particle. It gets attracted and repelled to a certain direction. Is this contributing negative or positive potential energy?

I've had a lot of partial insights but no complete solution. Thanks

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sniper_spike said:

V = kQ/r
PE = Vq

## The Attempt at a Solution

Tried a lot of ways... get an order of magnitude less than the answer and also off by a bit too.

Please help. I think you are supposed to take V at each location then multiply by q since this is PE.
V due to what? Multiply by which q ?
I carry everything in vector form but my numbers are confusing. Attraction is supposed to be negative PE. Well we have attraction/ repulsion both working on a particle. It gets attracted and repelled to a certain direction. Is this contributing negative or positive potential energy?

I've had a lot of partial insights but no complete solution. Thanks
What do you get for V at the location of Q1, for example?

V at Q1 should be..
k5.3e-6 *(-1.5i - 1.5j)  k3.7e-6 *(1.5i - 3j)
----------------- + -------------
1.5^2 + 1.5^2 ` 1.5^2 + 3^2

= -15900i - 15900j + 4440i - 8880j

= -11460i -24780j
= 27301r N*m/C

I mean q at that location.

So |PE| would be qV = 27301* 2.8e-6 = 0.0764 J

sniper_spike said:
V at Q1 should be..

= -15900i - 15900j + 4440i - 8880j
Voltage is a scalar.

haruspex said:
Voltage is a scalar.

Then how do i figure out the total voltage from two different particles?
I can only think of taking a scalar value between one charge and the point Q1,
and doing a scalar addition of that voltage with the voltage between the other and point Q2. Do i simply do this for all the particles to get a scalar total?

Last edited:
The voltage at one charge due to the other two is simply the sum of the voltages due to each of those two. But be careful re the total PE of a system with more than two charges. I would suggest imagining one charge moving away to infinity, then the other.

haruspex said:
The voltage at one charge due to the other two is simply the sum of the voltages due to each of those two. But be careful re the total PE of a system with more than two charges. I would suggest imagining one charge moving away to infinity, then the other.

your visualization seems to be the case. Thank you so much. Quite clear now.

Last edited:

## What is potential energy of a system of charged particles?

Potential energy of a system of charged particles is the amount of energy that a system of charged particles possesses due to their positions and interactions with each other. It is a form of energy that is stored in the system and can be converted into other forms of energy, such as kinetic energy.

## How is the potential energy of a system of charged particles calculated?

The potential energy of a system of charged particles is calculated using the formula U = k * (q1 * q2) / r, where k is the Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them. This formula is derived from the Coulomb's law, which describes the force between two charged particles.

## What factors affect the potential energy of a system of charged particles?

The potential energy of a system of charged particles is affected by the charges of the particles, the distance between them, and the medium in which they are located. The potential energy increases as the charges of the particles increase, and decreases as the distance between them increases. It also varies depending on the dielectric constant of the medium, which determines the strength of the electric field.

## What is the relationship between potential energy and electric potential?

The electric potential of a system of charged particles is the potential energy per unit charge. In other words, it is the potential energy that a unit charge would possess at a certain point in the system. Therefore, the electric potential is directly proportional to the potential energy, and both can be used interchangeably to describe the energy of the system.

## Can potential energy of a system of charged particles be negative?

Yes, the potential energy of a system of charged particles can be negative. This occurs when the particles have opposite charges and are separated by a distance greater than infinity (i.e. infinite distance). In this case, the force between the particles is attractive and the potential energy is negative, indicating that work would need to be done to bring the particles closer together.

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