# Potential Due to a Collection Charges

• simo
In summary, potential due to two charges can be calculated using the formula 1/(4πє) ∑ q/r, where r is the distance from each charge and direction is not relevant. It is a scalar quantity.

#### simo

My text reads for Potential Due to a Collection Charges:

1/(4πє) ∑ q/r

Lets say you want to calculate the potential between two charges. Do you take the magnitude of the distance (r) or do you account for their direction of the charges with respect to the field point.

Based on the examples I have seen, i seems like i should use the magnitude. However, it seems more logical to account for direction.

potential is a scalar

The potential due to two charges is exactly that given by the formula you provided, thus:
$$\frac{1}{4\pi\epsilon_0} (\frac{q_1}{r_1} + \frac{q_2}{r_2})$$

r_1 & r_2 are the distances from each charge. (Direction is not relevant, only distance from each charge.)

Woops, I didn't read the forum rules. I appreciate your help Doc Al. This won't happen again.

## 1. What is potential due to a collection of charges?

The potential due to a collection of charges is a measure of the amount of work needed to move a unit test charge from an infinite distance away to a specific point in an electric field created by a collection of charges.

## 2. How is the potential due to a collection of charges calculated?

The potential due to a collection of charges is calculated by summing up the individual potentials of each charge in the collection. The formula for calculating potential due to a point charge is V = kQ/r, where k is the Coulomb's constant, Q is the charge, and r is the distance between the charge and the point where potential is being measured.

## 3. How does the potential due to a collection of charges affect the behavior of charged particles?

The potential due to a collection of charges determines the direction and strength of the electric field at any point. Charged particles will experience a force in the direction of the electric field, and the magnitude of this force is determined by the potential difference between two points.

## 4. Can the potential due to a collection of charges be negative?

Yes, the potential due to a collection of charges can be negative. This means that work is required to move a test charge towards the collection of charges, and the test charge will lose potential energy as it moves closer to the collection of charges.

## 5. How does the distance between charges affect the potential due to a collection of charges?

The potential due to a collection of charges is inversely proportional to the distance between the charges. As the distance increases, the potential decreases, and vice versa. This means that the potential due to a collection of charges will decrease as the charges move further apart and increase as they move closer together.