Electrostatics Question 719
Question: A point charge $ 50\mu C $ is located in the x-y plane at a point whose position vector is $ \vec{r}=( 2\hat{i}+3\hat{j} )m. $ Then electric field at the point whose position vector is $ \vec{r}=( 8\hat{i}-5\hat{j} )m. $ (in vector form) will be
Options:
A) $ 90( -3\hat{i}+4\hat{j} )V/m $
$ $
B) $ 900( 3\hat{i}-4\hat{j} )V/m $
C) $ 90( 3\hat{i}-4\hat{j} )V/m $
D) (d)$ 900( -3\hat{i}+4\hat{j} )V/m $
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Answer:
Correct Answer: B
Solution:
[b] $ \vec{E}=\frac{kQ}{r^{3}}\vec{r}=\frac{9\times 10^{9}\times 50\times {{10}^{-6}}}{|\vec{r}-{{{\vec{r}}} _{0}}{{|}^{3}}}\times ( \vec{r}-{{{\vec{r}}} _{0}} ) $
Where $ \vec{r}-{{\vec{r}} _{0}}=(8\hat{i}-5\hat{j})-(2\hat{i}+3\hat{j})=6\hat{i}-8\hat{j} $
$ \vec{E}=900(3\hat{i}-4\hat{j})V/m $
