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Q.

A positive point charge $50 μ C$ is located in the plane x y at a point with radius vector ${\vec{r}}_{0} = 2 \hat{i} + 3 \hat{j}$ . Evaluate the electric field vector $\vec{E}$ at a point with radius vector $\vec{r} = 8 \hat{i} - 5 \hat{j}$ , where $r_{0}$ and r are expressed in meters.

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a

$(1.4 \hat{i} - 2.6 \hat{j}) k N C^{- 1}$

b

$(1.4 \hat{i} + 2.6 \hat{j}) k N C^{- 1}$

c

$(2.7 \hat{i} - 3.6 \hat{j}) k N C^{- 1}$

d

$(2.7 \hat{i} + 3.6 \hat{j}) k N C^{- 1}$

answer is C.

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Detailed Solution

$\vec{E} = \frac{1}{4 π ε_{0}} \frac{q}{{(r - r_{0})}^{3}} (\vec{r} - {\vec{r}}_{0})$

$\vec{r} - {\vec{r}}_{0} = (8 \hat{i} - 5 \hat{j}) - (2 \hat{i} + 3 \hat{j})$ = $(6 \hat{i} - 8 \hat{j})$

$| \vec{r} - {\vec{r}}_{0} | = \sqrt{6^{2} + 8^{2}} = 10 m$

$\vec{E} = 9 \times 10^{9} \times \frac{50 \times 10^{- 6}}{{(10)}^{3}} (6 \hat{i} - 8 \hat{j})$

$\vec{E} = (2.7 \hat{i} - 3.6 \hat{j}) k N C^{- 1} E = \sqrt{{(2700)}^{2} + {(3600)}^{2}}$

$E = 4500 N C^{- 1}$

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A positive point charge 50μC is located in the plane x y at a point with radius vectorr→0=2i^+3j^ . Evaluate the electric field vector E→ at a point with radius vectorr→=8i^−5j^ , where r0 and r are expressed in meters.