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Enter values

Pick what you want to compute. Enter the other quantities (with units).

Charges can be positive or negative. Example: q_1 = +2 µC, q_2 = −1 µC, r = 10 cm.

Tip: If solving for F, you can leave F blank. If solving for q₁/q₂/r, enter F.

Options:

Chips prefill inputs and calculate immediately.

Result:

No results yet. Enter values and click Calculate.

How to use this calculator

  • Choose what to solve for (F, q₁, q₂, or r).
  • Enter the other values with units (charges can be ±).
  • Click Calculate to compute the missing quantity.
  • Turn on Steps to see conversions and the substituted formula.

How this calculator works

  • Converts inputs to base SI units: C, m, N.
  • Uses Coulomb’s law F = k\frac{|q_1 q_2|}{r^2} with k = 8.9875517923\times10^9.
  • Determines attraction vs. repulsion from the signs of q₁ and q₂.

Formula & Equation Used

Coulomb’s law: F = k \dfrac{|q_1 q_2|}{r^2}

Solve for distance: r = \sqrt{k \dfrac{|q_1 q_2|}{F}}

Solve for charge: |q_1| = \dfrac{F r^2}{k |q_2|} (sign comes from direction choice)

Example Problems & Step-by-Step Solutions

Example 1 — +2 µC and −1 µC separated by 10 cm

  1. Convert to SI: \( q_1=2\times10^{-6}\,C,\; q_2=-1\times10^{-6}\,C,\; r=0.10\,m \).
  2. Compute magnitude with Coulomb’s law: \( F = k \dfrac{|q_1 q_2|}{r^2} \).
  3. Substitute and calculate: \( F = (8.99\times10^9)\dfrac{|(2\times10^{-6})(1\times10^{-6})|}{(0.10)^2} \approx 1.80\,N \).
  4. Signs are opposite, so the force is attractive.

Example 2 — Like charges repel: +1 µC and +1 µC separated by 5 cm

  1. Convert to SI: \( q_1=1\times10^{-6}\,C,\; q_2=1\times10^{-6}\,C,\; r=0.05\,m \).
  2. Substitute: \( F = (8.99\times10^9)\dfrac{|(1\times10^{-6})(1\times10^{-6})|}{(0.05)^2} \).
  3. Compute: \( F = (8.99\times10^9)\dfrac{1\times10^{-12}}{2.5\times10^{-3}} \approx 3.60\,N \).
  4. Both charges are positive, so the force is repulsive.

Example 3 — Solve for distance: q₁ = 3 µC, q₂ = 2 µC, and F = 0.54 N

  1. Convert to SI: \( q_1=3\times10^{-6}\,C,\; q_2=2\times10^{-6}\,C,\; F=0.54\,N \).
  2. Rearrange for distance: \( r=\sqrt{k\dfrac{|q_1q_2|}{F}} \).
  3. Substitute: \( r=\sqrt{(8.99\times10^9)\dfrac{|(3\times10^{-6})(2\times10^{-6})|}{0.54}} \).
  4. Compute: \( |q_1q_2|=6\times10^{-12} \), so \( r=\sqrt{\dfrac{(8.99\times10^9)(6\times10^{-12})}{0.54}}=\sqrt{0.0999}\approx 0.316\,m \).
  5. Convert if needed: \( 0.316\,m \approx 31.6\,cm \).

Frequently Asked Questions

Q: Why do we use absolute value in Coulomb’s law?

The formula gives the magnitude. Direction (attract vs repel) comes from the signs of the charges.

Q: What if my charges aren’t point charges?

Coulomb’s law is best when charge sizes are small compared to r. For extended objects, the field can vary across the object.

Q: What constant does the calculator use?

It uses k = 8.9875517923\times10^9\,N\cdot m^2/C^2.