# GRE Physics GR 1777 Problem Solution¶

## 039. Electrodynamics (Coulomb Force)¶

### You should know¶

#### Coulomb's Law¶

The electrostatics force $\vec{F}$ between two point charges $q_1$ and $q_2$ is

$$\large \vec{F} = k_e \frac{q_1 q_2}{r^2}\hat{r}$$

where

$k_e$: Coulomb's constant $(= \frac{1}{4\pi \epsilon_0})$

$q_{1,2}$: point charges

$r$: distance between the charges.

But in this question, it's not important.

#### Vector Sum¶

Since the electrostatic force is a vector, the net force is the result of adding all the forces together as vectors.

### Solution¶

$$\large \vec{F}_{d} = k_e \frac{e^2}{d^2} \hat{d}$$$$\large \vec{F}_{D} = k_e \frac{e^2}{D^2} \hat{D}$$

Thus,

$$\large \vec{F}_1 = \vec{F}_{d} + \vec{F}_{D}$$$$\large \vec{F}_2 = \vec{F}_{d} - \vec{F}_{D}$$$$\large \vec{F}_3 = \sqrt{\vec{F}^2_{d} + \vec{F}^2_{D} }$$

Therefore,

$$\large F_1 > F_3 > F_2$$

(C) $F_1 > F_3 > F_2$