First slide

Electric field

Question

A point charge of $100 μ C$ is placed at $(3 \hat{i} + 4 \hat{j}) m .$ Find the electric field intensity due to this charge at a point located at $(9 \hat{i} + 12 \hat{j}) m .$

Easy

A

8000 v/m
B

9000 v/m
C

2250 v/m
D

4500 v/m

Solution

(2)
$\begin{array}{l} {\vec{r}}_{A} = (3 \hat{i} + 4 \hat{j}) m, {\vec{r}}_{B} = (9 \hat{i} + 12 \hat{j}) m \\ ∴ {\vec{r}}_{B / A} = {\vec{r}}_{B} - {\vec{r}}_{A} = (6 \hat{i} + 8 \hat{j}) m \Rightarrow |{\vec{r}}_{B / A}| = \sqrt{6^{2} + 8^{2}} = 10 m \\ ∴ E_{B} = \frac{1}{4 π ε_{0}} \frac{Q}{{|{\vec{r}}_{B / A}|}^{2}} = 9 \times 10^{9} \times \frac{100 \times 10^{- 6}}{{(10)}^{2}} V / m = 9000 V / m \end{array}$

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