(1 point)
Suppose the electric field in space (units: N/C) is given in terms of cylindrical coordinates as follows:
$\mathbf{E} = \left( 12z\rho e^{-\rho^2} - \frac{12\cos\phi}{\rho^5} \right) \mathbf{a}_\rho - \frac{3\sin\phi}{\rho^5} \mathbf{a}_\phi - 6e^{-\rho^2} \mathbf{a}_z$.
Show
* that the work required to move a charge of 9 nC from
$(x, y, z) = (-3, 0, 5)$ to
$(x, y, z) = (0, -3, -1)$ is independent of the path taken, and find the work required.
ANSWER: Work = ____ J.
*Note: WeBWork has no way to assess your proof, so you can't enter it here. Be on the lookout for other opportunities to demonstrate the
knowledge this step requires.
