In the Coulomb force equation, does the magnitude of the force increase as the distance between the charged objects decrease ? Why or why not?
Yes, the magnitude of the force in the Coulomb's law equation increases as the distance between the charged objects decreases.
To understand why this happens, let's take a closer look at the equation for Coulomb's law:
\[ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
In this equation:
- F represents the magnitude of the force between two charged objects.
- k is the proportionality constant known as Coulomb's constant (k ≈ 9 × 10^9 N⋅m²/C²).
- q1 and q2 represent the magnitudes of the charges on the two objects.
- r represents the distance between the charges.
When the distance between the charged objects decreases (r becomes smaller), the denominator of the equation (r^2) becomes smaller as well. Since the other components of the equation (k, q1, and q2) remain constant, the overall force increases. This is because a decrease in the distance leads to a stronger electrostatic interaction between the charges.
Conversely, when the distance between the charged objects increases, the denominator becomes larger, resulting in a smaller force. Therefore, the magnitude of the force between charged objects is inversely proportional to the square of the distance between them, according to Coulomb's law.