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 A) x + y - 6z^-3. B) -y. C) -x. D) x + y.

Question

Quizplus · Accepted Answer

The electric field $\vec{E}$ is related to the potential $V$ by $\vec{E} = -\nabla V$, where $\nabla V$ is the gradient of $V$. The y-component of $\vec{E}$ is given by $-\frac{\partial V}{\partial y}$. For $V(x,y,z) = xy - 3z^{2}$, $-\frac{\partial V}{\partial y} = -x$, which corresponds to option C.

If the Potential in a Region Is Given by V(x,y,z)=