If potential(in volts ) in a region is expressed as V(x, y, z) = 6xy - y + 2yz , the electric field(in N C ^ - 1 ) at point(1, 1, 0) is

Correct answer: A. - (6 ^ i + 5 ^ j + 2 ^ k ) . V = 6xy - y + 2yz → E = - ((∂ V)/(∂ x) ^ i + (∂ V)/(∂ y) ^ j (∂ V)/(∂ z) ^ k ) → E = - [(6y) ^ i + (6x - 1 + 2z) ^ j + ( 2y ) ^ k ] → E ( 1, 1, 0 ) = - (6 ^ i + 5 ^ j + 2 ^ k )

NEET 2015

Exam: NEET
Year: 2015
Subject: Physics
Chapter: Electrostatics

NEET 2015 · Physics · Electrostatics

If potential(in volts ) in a region is expressed as V(x, y, z) =...

If potential(in

volts

) in a region is expressed as

V\left(x, y, z\right) = 6xy - y + 2yz

, the electric field(in

N{C}^{- 1}

) at point\left(1, 1, 0\right)$ is

Options

A $- \left(6\overset{^}{i} + 5\overset{^}{j} + 2\overset{^}{k}\right)$ .
B $- \left(2\overset{^}{i} + 3\overset{^}{j} + \overset{^}{k}\right)$ .
C $- \left(6\overset{^}{i} + 9\overset{^}{j} + \overset{^}{k}\right)$ .
D $- \left(3\overset{^}{i} + 5\overset{^}{j} + 3\overset{^}{k}\right)$ .

Correct answer

A. $- \left(6\overset{^}{i} + 5\overset{^}{j} + 2\overset{^}{k}\right)$ .

Step-by-step solution

$V = 6xy - y + 2yz$

$\overset{\to}{E} = - \left(\dfrac{∂ V}{∂ x}\overset{^}{i} + \dfrac{∂ V}{∂ y}\overset{^}{j}\dfrac{∂ V}{∂ z}\overset{^}{k}\right)$

$\overset{\to}{E} = - \left[\left(6y\right)\overset{^}{i} + \left(6x - 1 + 2z\right)\overset{^}{j} + ( 2y ) \overset{^}{k}\right]$

$\overset{\to}{E} ( 1, 1, 0 ) = - \left(6\overset{^}{i} + 5\overset{^}{j} + 2\overset{^}{k}\right)$

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