An Electric field E-3-5-k- exists in space- Find the potential difference between 1- 2- 1 and 4- 3- 5-

Given: E⃗=3î 5ĵ+k̂ nbsp; Points nbsp;(1, 2, 1) nbsp; and (4, 3, 5) We know that, Δ V= E.[Δ r] So, nbsp; Δ r=(4î+3ĵ+5k̂) (î+2ĵ+k̂) Δ r=(3î+ĵ+4k̂) Now, ...

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Standard XII

Physics

Potential Energy of a Dipole in Uniform Electric Field

An Electric f...

Question

An Electric field $\to E = 3^i - 5^j +^k$ exists in space. Find the potential difference between $(1, 2, 1)$ and $(4, 3, 5)$ .

4 V

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- 18 V

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6 V

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- 8 V

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Solution

The correct option is D $- 8 V$
Given:
$\to E = 3^i - 5^j +^k$
Points $(1, 2, 1)$ and $(4, 3, 5)$

We know that,
$Δ V = - \to E . [Δ r]$
So,
$Δ r = (4^i + 3^j + 5^k) - (^i + 2^j +^k)$

$Δ r = (3^i +^j + 4^k)$

Now, $Δ V = - (3^i - 5^j +^k) . (3^i +^j + 4^k)$

$Δ V = - (9 - 5 + 4) = - 8 V$

Hence, option $(D)$ is correct.

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An Electric field →E=3^i−5^j+^k exists in space. Find the potential difference between (1, 2, 1) and (4, 3, 5).

The correct option is D −8 V Given: →E=3^i−5^j+^k Points (1, 2, 1) and (4, 3, 5) We know that, ΔV=−→E.[Δr] So, Δr=(4^i+3^j+5^k)−(^i+2^j+^k) Δr=(3^i+^j+4^k) Now, ΔV=−(3^i−5^j+^k).(3^i+^j+4^k) ΔV=−(9−5+4)=−8 V Hence, option (D) is correct.

An Electric field $\to E = 3^i - 5^j +^k$ exists in space. Find the potential difference between $(1, 2, 1)$ and $(4, 3, 5)$ .