Graphing the Curl of -Cx\vec{z} on the xz plane

[scorpius1782]

I posted the divergence of this earlier but thought I should post the curl separately.

Homework Statement

Find the curl of $E=-Cx\hat{z}$

Homework Equations

∇xE=$[\frac{∂E_z}{∂y}-\frac{∂E_y}{∂z}]\hat{x}+[\frac{∂E_x}{∂z}-\frac{∂E_z}{∂x}]\hat{y}+[\frac{∂E_y}{∂x}-\frac{∂E_x}{∂y}]\hat{z}$

The Attempt at a Solution

Since there's only a z component
∇xE=$-\frac{∂E_z}{∂x}=C\hat{y}$

I'm suppose to graph this onto the xz plane. But, isn't all the same throughout the plane? I feel like maybe I missed a component from the derivatives but I think all the rest are 0, right?

Thanks for any guidance.

 

[HallsofIvy]

Yes, that is correct. For ever point the curl of $-Cx\vec{z}$ is the constant $C\vec{y}$.