# Graph curl onto the xz plane

1. Nov 12, 2013

### scorpius1782

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

1. The problem statement, all variables and given/known data

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

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

3. 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.

2. Nov 12, 2013

### HallsofIvy

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

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