# Electrical potential energy: 3 charges in a line

• alicemunro
In summary, the potential energy of three charges, q1, q2, and q3, can be calculated using the equation U = k(q1q2/r12 + q1q3/r13 + q2q3/r23), where k is the Coulomb constant and r12, r13, and r23 are the relative distances between the charges.
alicemunro

## Homework Statement

A positive charge, q1 is at (-20cm,0). An equal and opposite charge q2 is at (20cm, 0). A positive charge q3, equal to q1, is placed at (60cm,0). What is the potential energy of the three charges??

EPE= kq / r

## The Attempt at a Solution

EPE = k( (5 X 10^-9)/.2) + (5 X 10^-6)/.6) - (5 X 10^-6)/.2))

alicemunro said:

## Homework Statement

A positive charge, q1 is at (-20cm,0). An equal and opposite charge q2 is at (20cm, 0). A positive charge q3, equal to q1, is placed at (60cm,0). What is the potential energy of the three charges??

EPE= kq / r

## The Attempt at a Solution

EPE = k( (5 X 10^-9)/.2) + (5 X 10^-6)/.6) - (5 X 10^-6)/.2))
It looks like you have additional information to provide such as the charges of q1,q2, q3 also your equation for electric potential energy is incorrect should be:
$$U = k \frac{q_a q_b}{r_{ab}}$$
Finally I need to note that r is not the position but rather the relative distance between charges a and b. With these adjustments the answer should clear up a bit

I would first clarify the units of the given charges. Are they in Coulombs (C) or microCoulombs (μC)? This is important as it will affect the value of the constant k, which is the Coulomb's constant. Assuming the charges are in microCoulombs, the potential energy can be calculated as follows:

EPE = k(q1q2/r1 + q1q3/r2 + q2q3/r3)

Where k = 9 x 10^9 Nm^2/C^2 and r1 = 0.2m, r2 = 0.6m, r3 = 0.4m (distance between q2 and q3).

Substituting the values, we get:

EPE = (9 x 10^9)(5 x 10^-6)(5 x 10^-6)/0.2 + (9 x 10^9)(5 x 10^-6)(5 x 10^-6)/0.6 + (9 x 10^9)(5 x 10^-6)(5 x 10^-6)/0.4
= 225 J

Therefore, the potential energy of the three charges in a line is 225 Joules. It is important to note that potential energy is a scalar quantity and is always positive.

## 1. What is electrical potential energy?

Electrical potential energy is the energy that a charged particle possesses due to its position in an electric field. It is a form of potential energy that can be converted into other forms of energy, such as kinetic energy, when the charged particle moves within the electric field.

## 2. What are the units of electrical potential energy?

The units of electrical potential energy are joules (J) in the International System of Units (SI). However, it can also be measured in electron volts (eV) in some contexts, where 1 eV is equal to 1.602 × 10^-19 J.

## 3. How is electrical potential energy calculated?

The electrical potential energy of a system of charges can be calculated using the equation U = kQq/r, where k is the Coulomb constant (9 × 10^9 N·m^2/C^2), Q and q are the magnitudes of the two charges, and r is the distance between them.

## 4. Can electrical potential energy be negative?

Yes, electrical potential energy can be negative. This occurs when the two charges in the system have opposite signs, resulting in an attractive force between them. In this case, the potential energy is considered to be negative because work must be done to separate the charges and overcome the attractive force.

## 5. How does the arrangement of charges affect electrical potential energy?

The arrangement of charges can significantly affect the electrical potential energy of a system. In the example of three charges in a line, the potential energy will be different depending on the distance between the charges and the order in which they are arranged. Generally, the closer the charges are and the more symmetric the arrangement, the lower the potential energy will be.

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