Electric field,

$\overline{){\mathbf{E}}{\mathbf{=}}\frac{\mathbf{k}\mathbf{q}}{{\mathbf{r}}^{\mathbf{2}}}}$

Vector magnitude:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{r}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathbf{r}}_{\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{r}}_{\mathbf{y}}}^{\mathbf{2}}}}$

Direction for angles measured from the x-axis:

$\overline{){\mathbf{tan}}\mathbf{}{\mathbf{\theta}}{\mathbf{=}}\frac{{\mathbf{r}}_{\mathbf{y}}}{{\mathbf{r}}_{\mathbf{x}}}}$

Resolving vector components:

$\overline{)\begin{array}{rcl}{\mathbf{E}}_{\mathbf{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{E}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathbf{\theta}\\ {\mathbf{E}}_{\mathbf{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathbf{E}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathbf{\theta}\end{array}}$

**a)**

r_{1} = (-16.0 i + 12 j ) m (the vector moves in the negative x-direction)

$\begin{array}{rcl}\mathbf{\left|}{\stackrel{\mathbf{\rightharpoonup}}{\mathbf{r}}}_{\mathbf{1}}\mathbf{\right|}& \mathbf{=}& \sqrt{{{\mathbf{r}}_{\mathbf{1}\mathbf{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbf{r}}_{\mathbf{1}\mathbf{y}}}^{\mathbf{2}}}\\ & \mathbf{=}& \sqrt{{\mathbf{(}\mathbf{-}\mathbf{16}\mathbf{.}\mathbf{0}\mathbf{)}}^{\mathbf{2}}\mathbf{+}{\mathbf{(}\mathbf{12}\mathbf{.}\mathbf{0}\mathbf{)}}^{\mathbf{2}}}\end{array}$

|r_{1}| = 20 m

θ_{1} = tan^{-1} (r_{1}_{y}/r_{1}_{x}) = tan^{-1} (12/-16) = -36.9° (negative x-component shows that the angle is above the the negative x-axis).

From the positive x-axis:

θ_{1} = 180 - 36.9 = 143.1

r_{2} = (9 i + 12 j) m (the vector moves in the positive x-direction)

Two point charges are placed on the x-axis. The first charge, q_{1} = 8.00 nC, is placed a distance 16.0 m from the origin along the positive x-axis; the second charge, q_{2} = 6.00 nC, is placed a distance 9.00 m from the origin along the negative x-axis.

(a) Calculate the electric field at point A, located at coordinates (0 m, 12.0 m).

(b) Give the x and y components of the electric field as an ordered pair.

Express your answer in newtons per coulomb to three significant figures.

E_{Ax}, E_{Ay} =

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