Question

If throughout a particular region of space the potential can be expressed as $\mathit{V}\mathbf{}\mathbf{=}\mathbf{}\mathbf{4}\mathit{x}\mathit{z}\mathbf{}\mathbf{+}\mathbf{}\mathbf{2}\mathit{y}\mathbf{}\mathbf{-}\mathbf{}\mathbf{5}\mathit{z}$, what are the vector components of the electric field at location $\left(x,y,z\right)$?

Short answer

The vector component of electric field at location$\left(x,y,z\right)$ is .

Step-by-step solution

Write the given data from the question.

The potential, $V=4xz+2y-5z$.

Determine the formulas to calculate the vector components of the electric field at location x,y,z.

The expression to calculate the vector component of electrical field is given as follows.

........ (i)

Calculate the vector components of the electric field at location x,y,z.

Calculate the electrical filed.

Substitute $4xz+2y-5z$for $V$into equation (i)

Hence the vector component of electric field at location $\left(x,y,z\right)$is .