Question

Coulomb’s Law in Vector Form.

Answer 1

It q₁ and q₂ be two point charges separated by a distance r in vacuum, the force on q₂ due to q₁ (F₂₁) is given by

Where \(\hat{r}_{12}\) is a unit vector, pointing from q₁ to q₂ .

The force, on q₁ due to q₂ , is given by

Here \(\hat{r}_{21}\) is a unit vector along the direction of the line directed from q₂ to q₁

\(\hat{r}_{12}\) and \(\hat{r}_{21}\) are clearly unit vectors in opposite directions. We can therefore, write

Here \(\hat{r}\) is the unit vector that would have ‘its origin’ at the source of the force. A positive magnitude of |F|, implies repulsion while a negative value of |F|, implies attraction between the two charges.