The electric potential over a particular region of space is given by the function

V$($x$,$y$,$z$)=10$ xz$2-3$ x$2$y $+8$ y$2$z$.$

a$.$ Find the expressions for the x$,$ y$,$ and z components of the electric field over this region of space. That is$,$ find Ex$,$ Ey$,$ and Ez$,$ and then write the electric field as a vector.

For your expressions to be graded correctly, be sure to do the following:

Simply the expressions completely and leave no spaces between coefficients, quantities, and mathematical symbols.

Use the $"*"$ symbol for multiplication between every cofficient and quantity and between quantities when you type in your expressions. Use $"^"$ for exponents.

b$.$ Determine the magnitude of the electric field at the point P$(5,3,-8).$