Check the dimensional correctness of F = q₁q₂/(4πε₀r²)
Coulomb's law. The force between two point charges a distance r apart.
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
F = q1 q2 / (4 π ε0 r2)F[M L T-2]=q1 q2 / (4 pi epsilon0 r2)[M L T-2]Step by step
1. What each symbol stands for
- F force [M L T-2]
- q1 electric charge [T A]
- q2 electric charge [T A]
- ε0 permittivity of free space [M-1 L-3 T4 A2]
- r length [L]
2. The dimensions of each term
- F [M L T-2] [M L T-2]
- q1 q2 / (4 pi epsilon0 r2) [T A] × [T A] / (4 × π × [M-1 L-3 T4 A2] × [L]2) [M L T-2]
3. Compare
Every term has dimensions [M L T-2], so the equation is dimensionally consistent.
What it proves and what it does not
It can show
- Every term that is added or subtracted has the same dimensions, so the sum makes sense.
- Both sides of the equals sign have the same dimensions.
- Angles inside sin, cos and similar functions are pure numbers.
It cannot show
- A pure number such as 1/2 or 2π has no dimensions, so a check cannot see a missing or wrong one.
- Two quantities with the same dimensions, such as work and torque, cannot be told apart.
- A sign error or a wrong power that keeps the dimensions equal goes unnoticed.
Matching dimensions are necessary but not sufficient. Pure numbers such as 1/2 or 2π have no dimensions, so a check cannot see them, and an equation with matching dimensions can still be wrong.
Look up each quantity
F = q₁q₂/(4πε₀r²): quick answers
Is F = q₁q₂/(4πε₀r²) dimensionally correct?
Yes. Every term has the same dimensions, [M L T⁻²], so F = q₁q₂/(4πε₀r²) is dimensionally consistent. That does not prove the equation itself is correct.
Does a dimension check prove F = q₁q₂/(4πε₀r²) is right?
No. A check can show that an equation is wrong, but it cannot show that it is right. Pure numbers such as 1/2 and 2π have no dimensions, so the check cannot see them.