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Question

In an electric filed, potential at a point with position vector r is given by v =343|r|. The electric field at r = 3i+2j+6k is

A
21i+14j+42k
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B
3i+2j+6k
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C
3i+2j+6k7
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D
( 3i+2j+6k)
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Solution

The correct option is A 21i+14j+42k
Electric field at any point is given by,
E=dvdr
ATQ, U=343|r|E=ddr{343|r|}=343r2
Now, |r|=9+4+36=49
|r|2=49.
E=7
Now, Electric field at point r will be given by
E=7.{r}
=21^i+14^j+42^k

Option (A) is the correct answer.

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