Two equal point charges of 1 µC each are located at points ( $\hat{i} + \hat{j} + \hat{k}$ ) m and ( $2 \hat{i} + 3 \hat{j} - \hat{k}$ ) m. What is the magnitude of electrostatic force between them?

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10^-12 N

10^-6 N

10^-9 N

10^-3 N

answer is A.

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Detailed Solution

$r = (2 \hat{i} + 3 \hat{j} + \hat{k}) - (\hat{i} + \hat{j} - \hat{k}) m = (\hat{i} + 2 \hat{j} + 2 \hat{k}) m$

The magnitude of r is

$r = \sqrt{1^{2} + 2^{2} + 2^{2}} = \sqrt{1 + 4 + 4} = 3 m$

$∴ F = \frac{1}{4 {πε}_{0}} . \frac{q_{1} q_{2}}{r^{2}} = \frac{9 \times 10^{9} \times 10^{- 6} \times 10^{- 6}}{{(3)}^{2}} = 10^{- 3} N$

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