Ch.5 - Thermochemistry

Problem 26a

Chapter 5, Problem 26a

Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance r1, as shown in the accompanying illustration. Suppose they are separated to a larger distance r2, by moving them apart. (a) What change, if any, has occurred in the potential energy of the system?

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Identify the formula for the electric potential energy between two point charges: $U = \frac{k \cdot q_1 \cdot q_2}{r}$, where $k$ is Coulomb's constant, $q_1$ and $q_2$ are the charges, and $r$ is the separation distance.

Recognize that the potential energy $U$ is inversely proportional to the distance $r$ between the charges.

Consider the initial potential energy $U_1$ when the distance is $r_1$: $U_1 = \frac{k \cdot q_1 \cdot q_2}{r_1}$.

Consider the new potential energy $U_2$ when the distance is increased to $r_2$: $U_2 = \frac{k \cdot q_1 \cdot q_2}{r_2}$.

Compare $U_1$ and $U_2$: Since $r_2 > r_1$, $U_2 < U_1$, indicating that the potential energy of the system has decreased.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Potential Energy

Electric potential energy is the energy stored in a system of charged particles due to their positions relative to each other. For two point charges, this energy is given by the formula U = k * (q1 * q2) / r, where k is Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them. As the distance increases, the potential energy decreases for opposite charges, indicating that work is done against the electric force.

Coulomb's Law

Coulomb's Law describes the force between two charged objects, stating that the force 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 helps to understand how the force changes as the distance between the charges changes, which in turn affects the potential energy of the system.

Work and Energy Transfer

In physics, work is defined as the energy transferred when a force is applied over a distance. When the charged spheres are moved apart, work is done against the electric force, resulting in a change in potential energy. This concept is crucial for understanding how energy is conserved and transformed in electrostatic systems, particularly when charges are separated or brought closer together.

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