# Electrostatic Potential Energy

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In summary, the electrostatic potential energy of an isolated spherical conductor of radius 24 cm that is charged to 3.9 kV is approximately 0.36 J. This can be found by using the equation U = (kQ)/r, where k is the Coulomb constant (8.99 * 10^9 Nm^2/C^2), Q is the charge on the sphere, and r is the radius of the sphere. Alternatively, you can use the formula W = 1/2*V^2*R/k to calculate the potential energy as 1/2*V^2*R/k = 0.36 J.
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## Homework Statement

What is the electrostatic potential energy of an isolated spherical conductor of radius 24 cm that is charged to 3.9 kV?

## Homework Equations

Electric potential

U = (kQ)/r

## The Attempt at a Solution

U = ((8.99 * 109 ) * (3.9 * 103)/(0.24)

Could someone walk me through how to do this? Its a simple problem I know...but I'm not understanding it, thanks!

You may be confusing kV with Coulombs here.

The Voltage is your electrostatic potential energy and is supplied by the kQ/R relationship.

But they didn't give you the charge on the sphere.

The answer has to be formatted in Joules.. so its work, but I'm not exactly sure how to get work from an energy field.

So then you're wanting to know how much work is required to charge a sphere?

So Work = V * q

As you bring the charges to the sphere, there will be work for each charge carried in from ∞. The average ΔV will be 1/2*V that the charges will need to be brought in against. That means for all the charges the total work will be 1/2*V*Q - where Q is the total charge.

But we also know that V = kQ/R, so rewriting we have

W = 1/2*V*(V*R/k) = 1/2V2*R/k

Or if you looked at it like a capacitor - a spherical one floating in space - then you can start from Q = V*C and since the potential energy in a capacitor is 1/2Q2/C you can rewrite that as 1/2*k*Q2/R = 1/2*V2R/k

## 1. What is electrostatic potential energy?

Electrostatic potential energy is the potential energy stored in a system of charged particles due to their interactions with each other. It is a type of potential energy that arises from the electrical forces between charged particles.

## 2. How is electrostatic potential energy calculated?

The electrostatic potential energy is calculated using the formula U = kq1q2/r, where k is the Coulomb constant, q1 and q2 are the charges of the particles, and r is the distance between them.

## 3. What factors affect the electrostatic potential energy?

The electrostatic potential energy is affected by the charges of the particles, the distance between them, and the medium in which they are located. It also depends on the orientation of the charges and the presence of any external electric fields.

## 4. How does electrostatic potential energy relate to electric potential?

Electric potential is the amount of electrostatic potential energy per unit charge, and it is calculated by dividing the electrostatic potential energy by the charge of the particle. In other words, electric potential is a measure of the strength of the electric field at a specific point.

## 5. What is the significance of electrostatic potential energy in everyday life?

Electrostatic potential energy plays a crucial role in many technological applications, such as in the operation of electronic devices, power generation, and energy storage. It also helps us understand the behavior of charged particles in nature, such as lightning and static electricity.

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