Coulomb's Constant In Calculator Function

Coulomb's Constant Value:

\[ k = 8.987551789 \times 10^9 \, \text{N·m}^2/\text{C}^2 \]

Electrostatic Force (F):

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1. What is Coulomb's Constant?

Coulomb's constant (k) is a proportionality constant in Coulomb's law, which describes the electrostatic force between two charged particles. Its value is approximately 8.987551789 × 10⁹ N·m²/C².

2. How Does the Calculator Work?

The calculator uses Coulomb's law:

\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \]

Where:

\( F \) — Electrostatic force (Newtons)
\( k \) — Coulomb's constant (8.987551789 × 10⁹ N·m²/C²)
\( q_1, q_2 \) — Electric charges (Coulombs)
\( r \) — Distance between charges (meters)

Explanation: The force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

3. Importance of Coulomb's Constant

Details: Coulomb's constant is fundamental in electromagnetism, appearing in equations for electric fields, potential energy, and many other electromagnetic phenomena.

4. Using the Calculator

Tips: Enter the values of two charges in Coulombs and their separation distance in meters. The calculator will compute the electrostatic force between them.

5. Frequently Asked Questions (FAQ)

Q1: Why is Coulomb's constant so large?
A: The large value reflects the strength of electrostatic forces compared to gravitational forces at the atomic scale.

Q2: How is Coulomb's constant related to the vacuum permittivity?
A: \( k = \frac{1}{4\pi\epsilon_0} \), where \( \epsilon_0 \) is the vacuum permittivity.

Q3: Does Coulomb's constant change in different media?
A: The effective constant changes in different dielectrics, becoming \( k/\epsilon_r \) where \( \epsilon_r \) is the relative permittivity.

Q4: What are typical values for charges in calculations?
A: Elementary charge is ~1.602×10^-19 C. Macroscopic charges are typically in microcoulombs (µC) to millicoulombs (mC).

Q5: How accurate is this calculation for real-world applications?
A: The calculation is exact for point charges in a vacuum. For real-world applications, factors like charge distribution and medium properties must be considered.