If the electric field intensity is given by E-x-x-y-y-z-z Volt-m the potential difference between X2- 0- 0 and Y1- 2- 3 is

Ans :(c) V= ∫E.dl = [ ∫_1^2xdx+∫_2^0ydy+∫_3^0zdz] EQUATION = 12[2^2 1^2+0^2 2^2+0^2 3^2] = 12× 10=5 V ...

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Classification of Vector Fields and Important Vector Identities

If the electr...

Question

If the electric field intensity is given by
$\to E = (x {^u}_{x} + y {^u}_{y} + z {^u}_{z})$ Volt/m the potential difference between X(2, 0, 0) and Y(1, 2, 3) is

+1 volt

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-1 volt

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+5 volt

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+6 volt

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Solution

The correct option is C +5 volt
Ans :(c)

$V = - \int \to E . \to d l$

$= - [2 \int 1 x d x + 0 \int 2 y d y + 0 \int 3 z d z]$

EQUATION

$= - \frac{1}{2} [2^{2} - 1^{2} + 0^{2} - 2^{2} + 0^{2} - 3^{2}]$

$= - \frac{1}{2} \times - 10 = 5 V$

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If the electric field intensity is given by →E=(x^ux+y^uy+z^uz) Volt/m the potential difference between X(2, 0, 0) and Y(1, 2, 3) is

The correct option is C +5 voltAns :(c) V=−∫→E.→dl =−[2∫1xdx+0∫2ydy+0∫3zdz] EQUATION =−12[22−12+02−22+02−32] =−12×−10=5V

If the electric field intensity is given by
$\to E = (x {^u}_{x} + y {^u}_{y} + z {^u}_{z})$ Volt/m the potential difference between X(2, 0, 0) and Y(1, 2, 3) is

The correct option is C +5 volt
Ans :(c)

$V = - \int \to E . \to d l$

$= - [2 \int 1 x d x + 0 \int 2 y d y + 0 \int 3 z d z]$

EQUATION

$= - \frac{1}{2} [2^{2} - 1^{2} + 0^{2} - 2^{2} + 0^{2} - 3^{2}]$

$= - \frac{1}{2} \times - 10 = 5 V$