Figure 15.1: Example of Coulomb’s law in two dimensions. Here chargesq 1 ,q 2 , andq 3 at the vertices of
an isosceles right triangle;q 1 andq 2 are positive, andq 3 is negative. The total forceF 1 on chargeq 1 is the
vector sum of the forceF 12 onq 1 due toq 2 and the forceF 13 onq 1 due toq 3 :F 1 DF 12 CF 13.
If you know the angleof the unit vectorrO 12 (measured counterclockwise from theCxdirection), then
the unit vector in rectangular (cartesian) form is
Or 12 DcosiCsinj; (15.5)whereiandjare unit vectors in thexandydirections, respectively.
If there are multiple charges present, then thetotalforce on chargeq 1 is the vector sum of all the forces
on chargeq 1. For example, consider Fig. 15.1, which shows chargesq 1 ,q 2 , andq 3 at the vertices of an
isosceles right triangle. The total forceF 1 on chargeq 1 is the vector sum of the forceF 12 onq 1 due toq 2
and the forceF 13 onq 1 due toq 3 :F 1 DF 12 CF 13.
Appendix O gives a brief review of vector arithmetic.