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  4. A point charge q=100 μ C is located in the x-y plane at the point with position vector vecr0=2 hati+3 hatj+ hatk. What is the magnitude of electric field vector (in kV / m ) at the point with position vector vecr=8 hati-5 hatj+ hatk ?

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Q. A point charge $q=100\, \mu C$ is located in the $x-y$ plane at the point with position vector $\vec{r}_{0}=2 \hat{i}+3 \hat{j}+\hat{k}$. What is the magnitude of electric field vector (in $kV / m$ ) at the point with position vector $\vec{r}=8 \hat{i}-5 \hat{j}+\hat{k} ?$

Electric Charges and Fields

Solution:

Separation between two points,
$r=\sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}}=10\, m$
Now, $|\vec{E}|=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{r^{2}}$
Hence,
$E=\frac{9 \times 10^{9} \times 100 \times 10^{-6}}{100} V / m $
$=9000 \,V / m =9\, kV / m$