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Find out electric filed intensity at point $A(1,0,2)$ due to a point charge $-20\,\mu C$ situated at point $B(0, 2,1)$
$-22.5\times10^3 (\hat i - \sqrt 2\hat j + \hat k)$
$8.5\times10^3 (\hat i + \sqrt 2\hat j + \hat k)$
$22.5\times10^3 (\hat i + \sqrt 2\hat j - \hat k)$
$8.5\times10^3 (\hat i - \sqrt 2\hat j + \hat k)$
Solution
$\overrightarrow{\mathrm{r}}=\mathrm{P} . \mathrm{V} .$ of $\mathrm{A}-\mathrm{P} . \mathrm{V} .$ of $\mathrm{B}$
$=1 \hat{i}-\sqrt{2} \hat{j}+\hat{k}$
$|\overrightarrow{\mathrm{r}}|=\sqrt{1+(\sqrt{2})^{2}+1}=2$
$\overrightarrow{\mathrm{E}}=\frac{9 \times 10^{9} \times\left(-20 \times 10^{-6}\right)}{8}(\hat{i}-\sqrt{2} \hat{\mathrm{j}}+\hat{\mathrm{k}})$
$\overrightarrow{\mathrm{E}}=-22.5 \times 10^{3}(\hat{\mathrm{i}}-\sqrt{2} \hat{\mathrm{j}}+\hat{\mathrm{k}}) \mathrm{\,N} / \mathrm{C}$