Question

A charge of +3.00.uC (micro Coloumb) is located at the origin and a second charge of +2.00 pC (pico

Coloumb) is located on the xy plane at the point (x = 30.0cm , y = 20.0cm ). Determine the electric force

exerted by the 3.uC charge on the 2 pC charge.

Answer 1

Let $q_1=3\ \mu C$ and $q_2=2\ pC$. We can find the magnitude of the electric force on the 2 pC charge from the Coulomb's law:

$$F_{12}=\dfrac{kq_1q_2}{r_{12}^2},$$ $$F_{12}=\dfrac{8.99\cdot10^9\ \dfrac{Nm^2}{C^2}\cdot3.0\cdot10^{-6}\ C\cdot2\cdot10^{-12}\ C}{(\sqrt{(0.3\ m)^2+(0.2\ m)^2})^2},$$ $$F_{12}=4.15\cdot10^{-7}\ N.$$

We can find the direction of the electric force from the geometry:

$$\theta=tan^{-1}(\dfrac{0.2\ m}{0.3\ m})=33.7^{\circ}.$$

Answer:

$F_{12}=4.15\cdot10^{-7}\ N$, $33.7^{\circ}$ above the $x$-axis.