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Question

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

A

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

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B

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

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C

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

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D

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

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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 =−1.6×10−19 C →r=(2^i+^j)∴|→r|=√(2)2+(1)2=√5→E=Q→r4πε0r3=−1.6×10−19×9×109(√5)3(2^i+^j)→E=1.44×10−95√5(−2^i−^j)

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