Question

In an electric field the potential at a point is given by the following relation $V=\frac{343}{r}$ where r is distance from the origin. The electric field at $r=3\hat{i}+2\hat{j}+6\hat{k}$ is:

• A. $21\hat{i}+14\hat{j}+42\hat{k}$
• B. $3\hat{i}+2\hat{j}+6\hat{k}$
• C. $\frac{1}{7}(3\hat{i}+2\hat{j}+6\hat{k})$
• D. $-(3\hat{i}+2\hat{j}+6\hat{k})$

Answer 1

The correct option is D $-(3\hat{i}+2\hat{j}+6\hat{k})$

B. $3i+2j+6k$

Formula,

$E=\frac{V}{|\overrightarrow{r}|}\cdot \hat{r}$

$E=\frac{343}{|\overrightarrow{r}{|}^2}\cdot \frac{3i+2j+6k}{|r|}$

$=\frac{343}{7^2}\cdot \frac{3i+2j+6k}{7}$

$=3i+2j+6k$