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Question

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


A
21^i+14^j+42^k
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B
3^i+2^j+6^k
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C
17(3^i+2^j+6^k)
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D
(3^i+2^j+6^k)
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Solution

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

Formula,

$$E=\dfrac{V}{|\vec{r}|}\cdot \hat{r}$$

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

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

$$=3i+2j+6k$$

Physics

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