The electric A potential at a point (x, y, z) is given by $\mathrm{V}=-{\mathrm{x}}^2\mathrm{y}-{\mathrm{xz}}^3+4$ The electric field $\overrightarrow{\mathrm{E}}$at that point is

• A

  $\overrightarrow{\mathrm{E}}=\widehat{\mathrm{i}}\left(2\mathrm{xy}+{\mathrm{z}}^3\right)+\widehat{\mathrm{j}}{\mathrm{x}}^2+\widehat{\mathrm{k}}3{\mathrm{xz}}^2$

• B

  $\overrightarrow{\mathrm{E}}=\widehat{\mathrm{i}}2\mathrm{xy}+\widehat{\mathrm{j}}\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)+\widehat{\mathrm{k}}\left(3\mathrm{xz}-{\mathrm{y}}^2\right)$

• C

  $\overrightarrow{\mathrm{E}}=\widehat{\mathrm{i}}{\mathrm{z}}^3+\widehat{\mathrm{j}}\mathrm{xyz}+\widehat{\mathrm{k}}{\mathrm{z}}^2$

• D

  $\overrightarrow{\mathrm{E}}=\widehat{\mathrm{i}}\left(2\mathrm{xy}-{\mathrm{z}}^3\right)+\widehat{\mathrm{j}}{\mathrm{xy}}^2+\widehat{\mathrm{k}}3{\mathrm{z}}^2\mathrm{x}$