Static Electricity Formula Calculator

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

Charge 1 (\(q_1\)):

Charge 2 (\(q_2\)):

Distance Between Charges (\(r\)):

1. What is the Static Electricity Formula Calculator?

Definition: This calculator computes the electrostatic force (\(F\)) between two point charges (\(q_1\), \(q_2\)) separated by a distance (\(r\)) using Coulomb's Law, \(F = \frac{k q_1 q_2}{r^2}\), where \(k\) is Coulomb's constant (\(8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2\)).

Purpose: It is used in physics to determine the attractive or repulsive force between charged objects, applicable in studies of electric fields, capacitors, and particle interactions.

2. How Does the Calculator Work?

The calculator uses Coulomb's Law:

Formula: \[ F = \frac{k q_1 q_2}{r^2} \] where:

\(F\): Electrostatic force (N, mN, µN)
\(k\): Coulomb's constant (\(8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2\))
\(q_1\), \(q_2\): Charges (C, µC, nC)
\(r\): Distance between charges (m, cm)

Unit Conversions:

Charge:
- 1 C = 1 C
- 1 µC = \(10^{-6} \, \text{C}\)
- 1 nC = \(10^{-9} \, \text{C}\)
Distance:
- 1 m = 1 m
- 1 cm = 0.01 m
Force:
- 1 N = 1 N
- 1 mN = 0.001 N
- 1 µN = \(10^{-6} \, \text{N}\)

Steps:

Enter the charges (\(q_1\), \(q_2\)) and distance (\(r\)) with their units (default: \(q_1 = 1 \, \mu\text{C}\), \(q_2 = 1 \, \mu\text{C}\), \(r = 1 \, \text{m}\)).
Convert inputs to SI units (C, m).
Validate that the distance is greater than 0.
Calculate the force using Coulomb's Law.
Convert the force to the selected unit (N, mN, µN).
Display the result, rounded to 4 decimal places.

3. Importance of Static Electricity Calculation

Calculating electrostatic force is crucial for:

Physics: Understanding interactions between charged particles in electric fields and atomic systems.
Engineering: Designing capacitors, electrostatic precipitators, and other devices that rely on electric forces.
Education: Teaching Coulomb’s Law and the principles of electrostatics in physics.

4. Using the Calculator

Examples:

Example 1: Calculate the force for \(q_1 = 1 \, \mu\text{C}\), \(q_2 = 1 \, \mu\text{C}\), \(r = 1 \, \text{m}\), in N:
- Enter \(q_1 = 1 \, \mu\text{C}\), \(q_2 = 1 \, \mu\text{C}\), \(r = 1 \, \text{m}\).
- Convert: \(q_1 = 10^{-6} \, \text{C}\), \(q_2 = 10^{-6} \, \text{C}\).
- Force: \(F = \frac{(8.99 \times 10^9) \times (10^{-6}) \times (10^{-6})}{1^2} = 8.99 \times 10^{-3} \, \text{N}\).
- Result: \( \text{Electrostatic Force} = 0.0090 \, \text{N} \).
Example 2: Calculate the force for \(q_1 = 2 \, \text{nC}\), \(q_2 = -3 \, \text{nC}\), \(r = 10 \, \text{cm}\), in µN:
- Enter \(q_1 = 2 \, \text{nC}\), \(q_2 = -3 \, \text{nC}\), \(r = 10 \, \text{cm}\).
- Convert: \(q_1 = 2 \times 10^{-9} \, \text{C}\), \(q_2 = -3 \times 10^{-9} \, \text{C}\), \(r = 0.1 \, \text{m}\).
- Force: \(F = \frac{(8.99 \times 10^9) \times (2 \times 10^{-9}) \times (-3 \times 10^{-9})}{(0.1)^2} = \frac{-5.394 \times 10^{-8}}{0.01} = -5.394 \times 10^{-6} \, \text{N} = -5.394 \, \mu\text{N}\).
- Result: \( \text{Electrostatic Force} = -5.3940 \, \mu\text{N} \).

5. Frequently Asked Questions (FAQ)

Q: What does a negative force mean?
A: A negative force indicates an attractive force between opposite charges, while a positive force indicates repulsion between like charges.

Q: Why must the distance be greater than zero?
A: A zero distance would result in an infinite force, which is not physically meaningful at the charges’ positions.

Q: What is Coulomb’s constant?
A: Coulomb’s constant (\(k = 8.99 \times 10^9 \, \text{N·m}^2/\text{C}^2\)) is a proportionality constant that relates the force between charges to their magnitudes and separation.