In each of five situations, two point charges (Q1, Q2) are separated by a distance d . Rank them

step 1 In the given problem we have to arrange the electrostatic potential energy of the given systems

In each of five situations, two point charges (Q1, Q2) are...

In each of five situations, two point charges $\left(Q_{1}, Q_{2}\right)$ are separated by a distance $d .$ Rank them in order of the electric potential energy, from highest to lowest. (a) $Q_{1}=1 \mu C, Q_{2}=2 \mu C, d=1 \mathrm{m}$ (b) $Q_{1}=2 \mu \mathrm{C}, Q_{2}=-1 \mu \mathrm{C}, d=1 \mathrm{m}$ (c) $Q_{1}=2 \mu C, Q_{2}=-4 \mu C, d=2 m$ (d) $Q_{1}=-2 \mu \mathrm{C}, Q_{2}=-2 \mu \mathrm{C}, d=2 \mathrm{m}$ (e) $Q_{1}=4 \mu \mathrm{C}, Q_{2}=-2 \mu \mathrm{C}, d=4 \mathrm{m}$

In each of five situations, two point charges $\left(Q_{1}, Q_{2}\right)$ are separated by a distance $d .$ Rank them in order of the electric potential energy, from highest to lowest.
(a) $Q_{1}=1 \mu C, Q_{2}=2 \mu C, d=1 \mathrm{m}$
(b) $Q_{1}=2 \mu \mathrm{C}, Q_{2}=-1 \mu \mathrm{C}, d=1 \mathrm{m}$
(c) $Q_{1}=2 \mu C, Q_{2}=-4 \mu C, d=2 m$
(d) $Q_{1}=-2 \mu \mathrm{C}, Q_{2}=-2 \mu \mathrm{C}, d=2 \mathrm{m}$
(e) $Q_{1}=4 \mu \mathrm{C}, Q_{2}=-2 \mu \mathrm{C}, d=4 \mathrm{m}$

Key Concepts

Ranking Electric Potential Energy Based on Charge Configurations

When ranking multiple systems by electric potential energy, one must consider both the magnitude and the sign of the charges as well as their separation. By analyzing each configuration using the formula U = k(Q1*Q2)/d, one can compare the relative energies of the systems. This approach involves methodically calculating or comparing the products Q1*Q2 divided by the corresponding distances to establish a ranking from highest to lowest potential energy.

Distance Dependence in Electric Potential Energy

The electric potential energy is inversely related to the distance separating the charges. As the distance increases, the magnitude of the potential energy decreases, making the energy less sensitive to variations in the product of the charges. This concept is essential when comparing different charge configurations with varying distances between them.

Charge Sign and Interaction

The sign of the charges plays a critical role in determining the nature of the interaction. When the product Q1*Q2 is positive, the force is repulsive and the system has positive potential energy. When the product is negative, the force is attractive and the potential energy is negative. Understanding this is important for predicting energy states and behavior in multi-charge configurations.

Electric Potential Energy Formula

The electric potential energy between two point charges is given by the formula U = k(Q1*Q2)/d, where k is Coulomb's constant, Q1 and Q2 are the charges, and d is the separation between them. This formula encapsulates how the energy arises from the electrostatic interaction between charges, with the energy being directly proportional to the product of the charges and inversely proportional to the distance between them.

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