Force due to point charges is given by Coulomb's law:

$\overline{){\mathbf{F}}{\mathbf{=}}\frac{\mathbf{k}{\mathbf{q}}_{\mathbf{1}}{\mathbf{q}}_{\mathbf{1}}}{{\mathbf{r}}^{\mathbf{2}}}}$

2D vector magnitude:

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

2D vector direction:

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

Resolving a vector into its components:

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

**(1)**

r_{13}^{2} = (0.04^{2} + 0.302^{2})

q_{1} = 5.02 nC (10^{-9C}/1nC) = 5.02 × 10^{-9} C

q_{3} = 6.03 nC (10^{-9C}/1nC) = 6.03 × 10^{-9} C

A charge 5.02 nC is placed at the origin of an xy-coordinate system, and a charge -2.05 nC is placed on the positive x-axis at x = 4.00cm. A third particle, of charge 6.03 nC is now placed at the point x = 4.00 cm , y = 3.02 cm .

1. Find the *x*-component of the total force exerted on the third charge by the other two.

2. Find the *y*-component of the total force exerted on the third charge by the other two.

3. Find the magnitude of the total force acting on the third charge.

4. Find the direction of the total force acting on the third charge. ( *r**a**d**i**a**n**s* between *F*? and +*x*-axis )

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Coulomb's Law (Electric Force) concept. You can view video lessons to learn Coulomb's Law (Electric Force). Or if you need more Coulomb's Law (Electric Force) practice, you can also practice Coulomb's Law (Electric Force) practice problems.