5.3 Coulomb's law  (Page 4/11)

We can’t add these forces directly because they don’t point in the same direction: ${\overrightarrow{\text{F}}}_{12}$ points only in the − x -direction, while ${\overrightarrow{\text{F}}}_{13}$ points only in the + y -direction. The net force is obtained from applying the Pythagorean theorem to its x - and y -components:

where

and

We find that

at an angle of

that is, $58\text{°}$ above the − x -axis, as shown in the diagram.

Significance

It’s also worth noting that the only new concept in this example is how to calculate the electric forces; everything else (getting the net force from its components, breaking the forces into their components, finding the direction of the net force) is the same as force problems you have done earlier.

Summary

• Coulomb’s law gives the magnitude of the force between point charges. It is
  
  ${\overrightarrow{\text{F}}}_{12}(r)=\frac{1}{4\pi {\epsilon }_0}\frac{q_1{q}_2}{r_{12}^2}{\widehat{\text{r}}}_{12}$
  
  where $q_2$ and $q_2$ are two point charges separated by a distance r . This Coulomb force is extremely basic, since most charges are due to point-like particles. It is responsible for all electrostatic effects and underlies most macroscopic forces.

Conceptual questions

Problems