Electric field and potential: If the potential in a region is given by V(x,y,z) = xy - 3z^-2, then the y component of the electric field in that region is

Question

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The electric field $\vec{E}$ is related to the electric potential $V$ by the relation $\vec{E} = -\nabla V$, where $\nabla V$ represents the gradient of $V$. The gradient of a scalar field like $V(x,y,z)$ in three dimensions is given by $\nabla V = \left(\frac{\partial V}{\partial x}, \frac{\partial V}{\partial y}, \frac{\partial V}{\partial z}\right)$. For the y component of $\vec{E}$, we need to find $-\frac{\partial V}{\partial y}$. Given $V(x,y,z) = xy - 3z^-2$, $\frac{\partial V}{\partial y} = x$, so the y component of $\vec{E}$ is $-x$.

Electric Field and Potential: If the Potential in a Region