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Question: The electric potential at a point (x, y, z) is given by V = - x<sup>2</sup>y - xz<sup>3</sup> + 4. T...

The electric potential at a point (x, y, z) is given by V = - x2y - xz3 + 4. The electric field E→\overset{\rightarrow}{E} at that point is -

A

E→\overset{\rightarrow}{E}=i^\widehat{i}2xy + j^\widehat{j} (x2 + y2) +k^\widehat{k} (3xz - y2)

B

E→\overset{\rightarrow}{E}=i^\widehat{i}z3 + j^\widehat{j}xyz +k^\widehat{k}z2

C

E→\overset{\rightarrow}{E}=i^\widehat{i} (2xy - z3) +j^\widehat{j}xy2 +k^\widehat{k}3z2x

D

E→\overset{\rightarrow}{E}=i^\widehat{i} (2xy + z3) + j^\widehat{j}x2 +k^\widehat{k}3xz2

Answer

E→\overset{\rightarrow}{E}=i^\widehat{i} (2xy + z3) + j^\widehat{j}x2 +k^\widehat{k}3xz2

Explanation

Solution

Ex = - Ž Ey = - Ž Ez = - ∂V∂z\frac { \partial \mathrm { V } } { \partial \mathrm { z } }

\lang10250 = Ex i^\hat { \mathbf { i } } + Ey j^\hat { \mathrm { j } } + Ez k^\hat { \mathbf { k } }