Each of the following pairs of charges are separated by a...

Each of the following pairs of charges are separated by a distance $d$. Which pair has the highest potential energy? a) $+5 \mathrm{C}$ and $+3 \mathrm{C}$ d) $-5 \mathrm{C}$ and $+3 \mathrm{C}$ b) $+5 \mathrm{C}$ and $-3 \mathrm{C}$ e) All pairs have the $\begin{array}{ll}\text { c) }-5 \mathrm{C} \text { and }-3 \mathrm{C} & \text { same potential energy. }\end{array}$

Each of the following pairs of charges are separated by a distance $d$. Which pair has the highest potential energy?
a) $+5 \mathrm{C}$ and $+3 \mathrm{C}$
d) $-5 \mathrm{C}$ and $+3 \mathrm{C}$
b) $+5 \mathrm{C}$ and $-3 \mathrm{C}$
e) All pairs have the
$\begin{array}{ll}\text { c) }-5 \mathrm{C} \text { and }-3 \mathrm{C} & \text { same potential energy. }\end{array}$

Key Concepts

Electric Potential Energy

This concept describes the energy stored in a system of two point charges as a result of their positions relative to each other. The potential energy is determined by both the magnitude and the sign of the charges, as well as the distance between them, typically calculated using Coulomb's law.

Coulomb’s Law

Coulomb’s law governs the interaction between point charges, stating that the electric force (and consequently the potential energy) is proportional to the product of the magnitudes of the charges and inversely proportional to the distance between them. This law provides the formula that quantifies how potential energy scales with the charges and separation distance.

Effect of Charge Sign

The sign of the charges plays a crucial role in determining the potential energy. When both charges have the same sign, the potential energy is positive, indicating a repulsive interaction, while opposite signs yield a negative potential energy, indicating an attractive interaction. This difference is key when comparing systems with different pairs of charges.

Product of Charges

The potential energy between charges is proportional to the product of the two charge values. A larger positive product, as found in like-charge pairs with larger magnitudes, results in higher (more positive) potential energy compared to a smaller positive product or a negative product from unlike charges.

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