Find electric field at point (2, 1) due to an electron placed at the origin

$\vec{E}= \frac{1.44 \times 10^{-9}}{25} \left ( -2 \hat{i}- \hat{j} \ \right )$

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$\vec{E}= \frac{1.44 \times 10^{-9}}{5 \sqrt{5}} \left ( 2 \hat{i}+ \hat{j} \ \right )$

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$\vec{E}= \frac{1.44 \times 10^{-9}}{5 \sqrt{5}} \left ( -2 \hat{i}- \hat{j} \ \right )$

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$\vec{E}= \frac{1.44 \times 10^{-9}}{25} \left ( \hat{i} + 2 \hat{j} \ \right )$

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Solution

The correct option is C
$\vec{E}= \frac{1.44 \times 10^{-9}}{5 \sqrt{5}} \left ( -2 \hat{i}- \hat{j} \ \right )$

For a negative source charge, the electric field at point P points radially inwards.

In pur case Q $= - 1.6 \times 10^{- 19} C$

$\to r = (2^i +^j) ∴ | \to r | = \sqrt{(2)^{2} + (1)^{2}} = \sqrt{5} \to E = \frac{Q \to r}{4 π ε_{0} r^{3}} = \frac{- 1.6 \times 10^{- 19} \times 9 \times 10^{9}}{(\sqrt{5})^{3}} (2^i +^j) \to E = \frac{1.44 \times 10^{- 9}}{5 \sqrt{5}} (- 2^i -^j)$

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Find electric field at point (2, 1) due to an electron placed at the origin

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