Problem: A. What is the magnitude of the electric force on charge A in the figure?F=______NB. What is the direction of the electric force on charge A in the figure? Choose the best answer.(a) to the left(b) to the right(c) the force is zero

A. Electric force at point A is due to the charges at point B and C. 

We apply Coulomb's law between points A and B and again between points A and C.

$\boxed{\mathbf{F}\mathbf{=}\frac{{\mathbf{kq}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{2}}}{{\mathbf{r}}^{\mathbf{2}}}}$

Between A and B

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{A}\mathbf{B}}& \mathbf{=}& \frac{{\mathbf{kq}}_{\mathbf{A}}{\mathbf{q}}_{\mathbf{B}}}{{{\mathbf{r}}_{\mathbf{AB}}}^{\mathbf{2}}}\end{array}$

• k = 8.99 × 10⁹Nm²/C² (Coulomb's constant)
• q_A = 1.0 × 10^-9 C
• q_B = - 1.0 × 10^-9 C
• r_AB = 1 × 10^-3 m

Substituting:

$\begin{array}{rcl}{\mathbf{F}}_{\mathbf{AB}}& \mathbf{=}& \frac{\mathbf{(}\mathbf{8}\mathbf{.}\mathbf{99}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}{\mathbf{Nm}}^{\mathbf{2}}\mathbf{/}{\mathbf{C}}^{\mathbf{2}}\mathbf{)}\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{C}\mathbf{)}\mathbf{(}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{C}\mathbf{)}}{{\mathbf{(}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathbf{m}\mathbf{)}}^{\mathbf{2}}}\\ & \mathbf{=}& \frac{\mathbf{(}\mathbf{8}\mathbf{.}\mathbf{99}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{N}\cancel{{\mathbf{m}}^{\mathbf{2}}}\mathbf{/}\cancel{{\mathbf{C}}^{\mathbf{2}}}\mathbf{)}\mathbf{\left[}\mathbf{\right(}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\left)}\mathbf{\right(}\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{\left)}\mathbf{\right]}\cancel{{\mathbf{C}}^{\mathbf{2}}}}{\mathbf{1}\mathbf{.}\mathbf{0}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\cancel{{\mathbf{m}}^{\mathbf{2}}}}\end{array}$

F_AB =  - 8.99 × 10^-3 N