1. What is a Coulomb's Law Calculator?

Definition: This calculator computes the electrostatic force between two charged particles using Coulomb's Law, which quantifies the force as directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

Purpose: It is used in physics and engineering to determine the force of attraction or repulsion between charged particles, which is essential for understanding electric fields, designing electronic components, and analyzing atomic interactions.

2. How Does the Calculator Work?

The electrostatic force is calculated using:

Where:

• \( F \) is the electrostatic force (N)
• \( k_e \) is the Coulomb constant (\( 8.9875517923 \times 10^9 \, \text{N·m}^2/\text{C}^2 \))
• \( q_1, q_2 \) are the charges (C)
• \( r \) is the distance between the charges (m)

Steps:

• Enter the first charge (\( q_1 \)) and select a unit (pC, nC, µC, mC, C)
• Enter the second charge (\( q_2 \)) and select a unit (pC, nC, µC, mC, C)
• Enter the distance (\( r \)) and select a unit (pm, nm, µm, mm, cm, m)
• Convert charges and distance to C and m, respectively
• Calculate the force using the formula
• Convert the force to newtons (N), millinewtons (mN), micronewtons (µN), nanonewtons (nN), and piconewtons (pN)
• Determine if the force is attractive (opposite charges) or repulsive (like charges)

Display format:

• If a force value is greater than 10000 or less than 0.0001 in absolute terms (and not zero), it is displayed in scientific notation (e.g., \( 1.234567e-12 \))
• Otherwise, it is displayed in decimal format with 5 decimal places

3. Importance of Coulomb's Law Calculation

Details: Coulomb's Law is fundamental in electrostatics, describing the interaction between charged particles. It is crucial for understanding electric fields, designing capacitors, analyzing atomic and molecular structures, and developing technologies like photocopiers and laser printers. The law also highlights the inverse-square nature of electrostatic forces, similar to gravity, but with the key difference that it can be attractive or repulsive.

4. Using the Calculator

Tips: Enter the charges (\( q_1, q_2 \)) with their units and the distance (\( r \)) with its unit. The calculator will compute the electrostatic force in newtons (N), millinewtons (mN), micronewtons (µN), nanonewtons (nN), and piconewtons (pN), with 5 decimal places. If the force is greater than 10000 or less than 0.0001 in absolute terms, it will be displayed in scientific notation. It will also indicate whether the force is attractive (opposite charges) or repulsive (like charges).

Examples:

• \( q_1 = 2 \, \text{nC} \), \( q_2 = -4 \, \text{nC} \), \( r = 10 \, \text{mm} \):
  • \( q_1 = 2 \times 10^{-9} = 0.000000002 \, \text{C} \)
  • \( q_2 = -4 \times 10^{-9} = -0.000000004 \, \text{C} \)
  • \( r = 10 \times 10^{-3} = 0.01 \, \text{m} \)
  • \( F = (8.9875517923 \times 10^9) \times \frac{(0.000000002) \times (-0.000000004)}{(0.01)^2} = -0.00071900 \, \text{N} \)
  • mN = \( -0.71900 \)
  • µN = \( -719.00414 \)
  • nN = \( -7.19004e+05 \)
  • pN = \( -7.19004e+08 \)
  • Force Type: Attractive
• \( q_1 = 3 \, \text{µC} \), \( q_2 = 6 \, \text{µC} \), \( r = 0.288 \, \text{m} \):
  • \( q_1 = 3 \times 10^{-6} = 0.000003 \, \text{C} \)
  • \( q_2 = 6 \times 10^{-6} = 0.000006 \, \text{C} \)
  • \( r = 0.288 \, \text{m} \)
  • \( F = (8.9875517923 \times 10^9) \times \frac{(0.000003) \times (0.000006)}{(0.288)^2} = 1.95000 \, \text{N} \)
  • mN = \( 1950.00000 \)
  • µN = \( 1950000.00000 \)
  • nN = \( 1950000000.00000 \)
  • pN = \( 1.95000e+12 \)
  • Force Type: Repulsive
• \( q_1 = 1 \, \text{pC} \), \( q_2 = 1 \, \text{pC} \), \( r = 1 \, \text{pm} \):
  • \( q_1 = 1 \times 10^{-12} = 0.000000000001 \, \text{C} \)
  • \( q_2 = 1 \times 10^{-12} = 0.000000000001 \, \text{C} \)
  • \( r = 1 \times 10^{-12} = 0.000000000001 \, \text{m} \)
  • \( F = (8.9875517923 \times 10^9) \times \frac{(0.000000000001) \times (0.000000000001)}{(0.000000000001)^2} = 8.98755e+09 \, \text{N} \)
  • mN = \( 8.98755e+12 \)
  • µN = \( 8.98755e+15 \)
  • nN = \( 8.98755e+18 \)
  • pN = \( 8.98755e+21 \)
  • Force Type: Repulsive

5. Frequently Asked Questions (FAQ)

Q: What is Coulomb's Law?
A: Coulomb's Law describes the electrostatic force between two charged particles, stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

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

Q: Why are some force values displayed in scientific notation?
A: Values greater than 10000 or less than 0.0001 in absolute terms (and not zero) are displayed in scientific notation for clarity, as they would otherwise be difficult to read in decimal format.

Q: Why are force results shown in multiple units?
A: Force values can vary widely in magnitude. Displaying the result in newtons (N), millinewtons (mN), micronewtons (µN), nanonewtons (nN), and piconewtons (pN) provides flexibility for different applications, as some contexts may require smaller units like pN or µN.

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