Two positively charged spheres, each with a charge of 2.0⨉10^-5 C, a mass of 1.0 kg, and separated by a distance of 1.0 cm, are held in place on a frictionless track. (a) What is the electrostatic potential energy of this system?

Verified step by step guidance

1. Identify the formula for electrostatic potential energy between two point charges: \(U = \frac{k \cdot q_1 \cdot q_2}{r}\), where \(k\) is Coulomb's constant (\$8.99 \times 10^9 \text{ N m}^2/\text{C}^2\(), \)q_1\( and \)q_2\( are the charges, and \)r$ is the separation distance.
2. Substitute the given values into the formula: \(q_1 = q_2 = 2.0 \times 10^{-5} \text{ C}\) and \(r = 1.0 \times 10^{-2} \text{ m}\).
3. Calculate the product of the charges: \(q_1 \cdot q_2 = (2.0 \times 10^{-5} \text{ C}) \cdot (2.0 \times 10^{-5} \text{ C})\).
4. Substitute the values into the formula: \(U = \frac{8.99 \times 10^9 \text{ N m}^2/\text{C}^2 \cdot (2.0 \times 10^{-5} \text{ C})^2}{1.0 \times 10^{-2} \text{ m}}\).
5. Simplify the expression to find the electrostatic potential energy \(U\).

Key Concepts

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of charged particles due to their positions relative to each other. It can be calculated using the formula U = k * (q1 * q2) / r, where U is the potential energy, k is Coulomb's constant, q1 and q2 are the charges, and r is the distance between them. This concept is crucial for understanding how charged objects interact and the energy associated with their configuration.

Coulomb's Law

Coulomb's Law describes the force between two point charges. It states that the magnitude of the electrostatic force F between two charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in calculating the forces and potential energy in systems involving charged particles.

Units of Charge and Energy

In electrostatics, charge is measured in coulombs (C), while energy is typically measured in joules (J). Understanding these units is essential for performing calculations involving electrostatic potential energy. For instance, when calculating potential energy, one must ensure that the charges are in coulombs and the distance is in meters to obtain energy in joules, which is a standard unit of energy in physics.