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

• A

  $\vec{E}=\hat{i}\left(2 x y-z^3\right)+\hat{j} x y^2+\hat{k} 3 z^2 x$
• Correct answer
  B

  $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}}\left(2 x y+\mathrm{z}^3\right)+\hat{\mathrm{j}} \mathrm{x}^2+\hat{\mathrm{k}} 3 \mathrm{xz} \mathrm{z}^2$
• C

  $\vec{E}=\hat{i} 2 x y+\hat{j}\left(x^2+y^2\right)+\hat{k}\left(3 x z-y^2\right)$
• D

  $\overrightarrow{\mathrm{E}}=\hat{\mathrm{i}} z+\hat{\mathrm{j}} x y z+\hat{\mathrm{k}} z^2$

Hence, the correct answer is option: 'B'.