Vector Form of Coulomb's Law

Electrostatic Force

The force of attraction or repulsion between two stationary electric charges.

Unit Vector

A vector having a magnitude of unity (one), used to indicate direction.

Position Vector

A vector that represents the position of a point in space relative to an origin.

Vector form of Coulomb's Law (Force on q2 due to q1)

where \(\hat{r}_{21}\) is the unit vector pointing from q1 to q2.

\vec{F}_{21} = \frac{1}{4\π\varepsilon₀} \frac{q₁ q₂}{r²} \hat{r}_{21}

Vector form of Coulomb's Law (Force on q1 due to q2)

where \(\hat{r}_{12}\) is the unit vector pointing from q2 to q1. Note that \(\hat{r}_{12} = -\hat{r}_{21}\).

\vec{F}_{12} = \frac{1}{4\π\varepsilon₀} \frac{q₁ q₂}{r²} \hat{r}_{12}

Relationship between forces

Newton's third law applied to electrostatic forces.

\vec{F}_{12} = -\vec{F}_{21}

Unit vector

where \(\vec{r}\) is the position vector and |\(\vec{r}\)| is its magnitude (distance).

\hat{r} = \frac{\vec{r}}{|\vec{r}|}