First slide

Electric field

Question

A point charge q= -8.0 nC is located at the origin. The electric field (in NC^-1) vector at the point x = 1.2 m, y = -1.6 m, as shown in figure, is

Moderate

A

$- 14.4 \hat{i} + 10.8 \hat{j}$
B

$- 14.4 \hat{i} - 10.8 \hat{j}$
C

$- 10.8 \hat{i} + 14.4 \hat{j}$
D

$- 10.8 \hat{i} - 14.4 \hat{j}$

Solution

$\vec{E} = \frac{1}{4 π ε_{0}} \frac{q}{r^{2}} \hat{r}$
$\begin{array}{l} \hat{r} = \frac{\vec{r}}{r} = \frac{(1.2 - 0) \hat{i} + (- 1.6 - 0) \hat{j}}{\sqrt{(1.2)^{2} + (1.6)^{2}}} \\ \hat{r} = \frac{1}{2} (1.2 \hat{i} - 1.6 \hat{j}) \\ \vec{E} = 9 \times 10^{9} \times \frac{(- 8 \times 10^{- 9})}{2^{2}} \times [\frac{1}{2} (1.2 \hat{i} - 1.6 \hat{j})] \\ \vec{E} = - 10.8 \hat{i} + 14.4 \hat{j} {NC}^{- 1} \end{array}$

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