Question

Constants | Periodic Table : 12 μC (Figure Part A g2-32 μC ' and In the figure take gi : 69 1) Find the electric force on g3 Enter your answers numerically separated by a comma. Express your answers using two significant figures Figure < 1011 > Submit Request Answer y (m) Return to Assignment Provide Feedback O 13 71 42 x (m

Answer 1

Part A : The electric force on charge q₃ due to charge q₁ & charge q₂ which will be given as -

We know that, $\vec{F}$₃ = $\vec{F}$₁₃ + $\vec{F}$₂₃

$\vec{F}$₃ = (k_e q₁ q₃ / r₁₃²) $\hat{r}$₁₃ + (k_e q₂ q₃ / r₂₃²) $\hat{r}$₂₃

$\vec{F}$₃ = (k_e q₁ q₃ / r₁₃²) ($\vec{r}$₁₃ / |r₁₃|) + (k_e q₂ q₃ / r₂₃²) ($\vec{r}$₂₃ / |r₂₃|)

$\vec{F}$₃ = (k_e q₁ q₃ / | r₁₃ |³) $\vec{r}$₁₃ + (k_e q₂ q₃ / | r₂₃ |³) $\vec{r}$₂₃                                                                     { eq.1 }

From a given diagram, the vector between q₁ and q₃ is given as :

$\vec{r}$₁₃ = (2 m) $\hat{i}$ + (1 m) _$\hat{j}$

It's magnitude which will be given by -

| r₁₃ | = _$\sqrt{}$(2 m)² + (1 m)²

| r₁₃ | = _$\sqrt{}$5 m

From a given diagram, the vector between q₂ and q₃ is given as :

$\vec{r}$₂₃ = (2 m) _$\hat{j}$

It's magnitude which will be given by -

| r₂₃ | = _$\sqrt{}$(2 m)² + (0 m)²

| r₂₃ | = _$\sqrt{}$4 m²

| r₂₃ | = 2 m

Using eq.1 ;   $\vec{F}$₃ = (k_e q₁ q₃ / | r₁₃ |³) $\vec{r}$₁₃ + (k_e q₂ q₃ / | r₂₃ |³) $\vec{r}$₂₃     

$\vec{F}$₃ = {[(9 x 10⁹ Nm²/C²) (69 x 10^-6 C) (12 x 10^-6 C)] / (_$\sqrt{}$5 m)³} [(2 m) $\hat{i}$ + (1 m) _$\hat{j}$] + {[(9 x 10⁹ Nm²/C²) (-32 x 10^-6 C) (12 x 10^-6 C)] / (2 m)³} [(2 m) _$\hat{j}$]

$\vec{F}$₃ = [(7.452 Nm²) / (11.1 m³)] [(2 m) $\hat{i}$ + (1 m) _$\hat{j}$] - [(3.456 Nm²) / (8 m³)] [(2 m) _$\hat{j}$]

$\vec{F}$₃ = (0.671 N/m) [(2 m) $\hat{i}$ + (1 m) _$\hat{j}$] - (0.432 N/m) [(2 m) _$\hat{j}$]

$\vec{F}$₃ = [(1.342 N) $\hat{i}$ + (0.671 N) _$\hat{j}$ - (0.864 N) _$\hat{j}$]

$\vec{F}$₃ = [(1.342) $\hat{i}$ - (0.193) _$\hat{j}$] N

Answer in two significant figures :

$\vec{F}$_3,x = 1.3 N   ,   $\vec{F}$_3,y = 0.2 N

Therefore, magnitude of an electric force on charge q₃ which will be given as -

| $\vec{F}$₃ | = _$\sqrt{}$(1.342 N)² + (-0.193 N)²

| $\vec{F}$₃ | = _$\sqrt{}$1.838213 N²

| $\vec{F}$₃ | = 1.35 N