The electric force between two charges Q1 and Q2 a distance...

The electric force between two charges $Q_{1}$ and $Q_{2}$ a distance $r$ apart is given by $F=k \frac{Q_{1} Q_{2}}{r^{2}},$ where $k$ is a constant. (a) If both charges double, by what factor does the force between them increase? (b) If both charges double but the force between them stays the same, by what factor did their separation change?

The electric force between two charges $Q_{1}$ and $Q_{2}$ a distance $r$ apart is given by $F=k \frac{Q_{1} Q_{2}}{r^{2}},$ where $k$ is a constant.
(a) If both charges double, by what factor does the force between them increase?
(b) If both charges double but the force between them stays the same, by what factor did their separation change?

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Key Concepts

Coulomb's Law

Coulomb's law defines the electric force between two point charges as being directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This principle forms the basis for analyzing interactions between static charges.

Scaling Relationships in Physical Quantities

Scaling relationships describe how changes in one physical quantity, such as the magnitude of charges or separation distance, affect another, like the electric force. By applying proportionality rules, one can predict how variations in charge magnitude or distance influence the force, which is essential for solving problems in electrostatics.

Inverse-Square Dependence

The inverse-square dependence indicates that the force between two charges decreases with the square of the distance between them. This concept is crucial in many areas of physics because it explains how the impact of a field diminishes as one moves away from its source, emphasizing the geometric spreading of the force.

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