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

The correct option is A 21i⃗+14j⃗+42k⃗ Electric field at any point is given by, #160; #160; #160; #160; #160; #160; #160; #160; # ...

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Standard XII

Physics

Gravitational Potential

In an electri...

Question

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

21 \to i + 14 \to j + 42 \to k

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3 \to i + 2 \to j + 6 \to k

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\frac{3 \to i + 2 \to j + 6 \to k}{7}

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- (3 \to i + 2 \to j + 6 \to k)

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Solution

The correct option is A $21 \to i + 14 \to j + 42 \to k$
Electric field at any point is given by,
$\to E = \frac{- d v}{d r}$
ATQ, $U = \frac{343}{| \to r |} ∴\Rightarrow ∣ ∣ \to E ∣ ∣ = \frac{- d}{d r} {\frac{343}{| \to r |}} = \frac{343}{∣ ∣ {\to r}^{2} ∣ ∣}$
Now, $| \to r | = \sqrt{9 + 4 + 36} = \sqrt{49}$
${| \to r |}^{2} = 49.$
$\Rightarrow ∣ ∣ \to E ∣ ∣ = 7$
Now, Electric field at point $\to r$ will be given by
$\to E = 7. {\to r}$
$= 21^i + 14^j + 42^k$

$∴$ Option (A) is the correct answer.

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

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