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

$8000 {Vm}^{- 1}$
B

$9000 {Vm}^{- 1}$
C

$2250 {Vm}^{- 1}$
D

$4500 {Vm}^{- 1}$

Solution

Position vector of point with respect to point charge is
$\begin{array}{l} \vec{r} = (9 - 3) \hat{i} + (12 - 4) \hat{j} = 6 \hat{i} + 8 \hat{j} \\ or r = \sqrt{6^{2} + 8^{2}} = 10 m \\ E = \frac{9 \times 10^{9} \times 100 \times 10^{- 6}}{10^{2}} = 9000 {Vm}^{- 1} \end{array}$

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