Q: A point charge of 100 μC is placed at $ \displaystyle 3 \hat{i} + 4 \hat{j} $ m. Find the electric field intensity due to this charge at a point located at $ \displaystyle 9 \hat{i} + 12 \hat{j} $ m

(a) 8000 Vm^{-1}

(b) 9000 Vm^{-1}

(c) 2250 Vm^{-1}

(d) 4500 Vm^{-1}

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Ans: (b)

Sol: $\displaystyle \vec{r}= (9 \hat{i} + 12 \hat{j}) – (3 \hat{i} + 4 \hat{j}) $ m

$ \displaystyle = 6 \hat{i} + 8 \hat{j} $

$\displaystyle r = \sqrt{6^2 + 8^2} $

r = 10 m

$ \displaystyle E = \frac{1}{4 \pi \epsilon_0}. \frac{q}{r^2} $

$ \displaystyle E = 9 \times 10^9 \frac{100 \times 10^{-6}}{10^2} $

E = 9000 V/m