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The electric force is a fundamental concept in physics, depicting the force exerted between charged objects. It's a fascinating interaction, acting both as an attractive and repulsive force, depending on the nature of the charges involved. When you have two objects with opposite charges, the electric force is attractive, pulling them towards each other. Conversely, with like charges, they repel. This force operates over a distance, much like gravity, and its strength diminishes with increased separation between the charges.

In this exercise, we explore the electric force between two humans each carrying a 1.0 Coulomb charge—one positive and one negative. The scenario sets them at a distance where this electric attraction equals the gravitational force exerted by their weight. This unique setup allows us to delve into how electric forces scale with distance and charge magnitude, illustrating their power even when compared to everyday forces like weight.

Gravitational force is the natural force of attraction experienced between two masses. On Earth, it's responsible for giving us weight and keeping us grounded. It’s described by Newton’s Law of Universal Gravitation, but in everyday circumstances, it's what makes us perceive our weight as the force with which Earth attracts us. This force is always attractive and acts over long distances, drawing masses toward each other.

In the context of this physics problem, the gravitational force that equals 650 N is the weight of an average human. The problem challenges us to find the distance where the electric force between the charged individuals equals this force. This comparison highlights how electric forces can overpower gravitational ones when charges are significant, despite often being overlooked in daily life.

Coulomb's constant, symbolized as \( k \), is a crucial figure in electrostatics, appearing in Coulomb's Law. It quantifies the proportionality between electric force, charge magnitudes, and distance between charges. With a value of \( 8.99 \times 10^9 \text{ N m}^2/ ext{C}^2 \), it shows the intensity with which electric forces act at a given distance.

This constant plays a vital role in calculating the electric force between two point charges. In the given exercise, knowing Coulomb's constant allows us to bridge the gap between theoretical charge interactions and practical calculations. It's the backbone of determining how intense the force will be for the specific setup of charges. By incorporating this constant into calculations, we precisely determine the distance at which the electric force matches the gravitational pull on the humans.

Physics problem-solving often involves understanding underlying principles and applying formulas judiciously. In exercises like this one, step-by-step approaches are vital. Here's how we systematically tackled the presented problem:

• **Understanding the problem:** Identifying that we need the electric force to equal a specific gravitational force and noting variables, like charge and force magnitude.
• **Using Coulomb’s Law:** Applying the formula \( F = k \frac{|q_1 q_2|}{r^2} \) helps set up the problem in a solvable equation by substituting known values.
• **Rearranging and solving:** This involves isolating the variable of interest—in this case, distance \( r \)—from the equation through rearrangement and substitution.
• **Calculating results:** Finally, performing mathematical calculations to arrive at numerical results, ensuring logical consistency throughout.

By following this logical sequence, physics becomes a methodical process of exploration, where we transform theoretical concepts into practical understanding.