Is Charge Density Zero for a Uniform E-field in y-direction?

[AdkinsJr]

Homework Statement

I have a function for an E-field $$E(x,y,z,t)=E_o\cos(k(x-ct))\hat j$$ and I need to find the charge density...

Homework Equations

$$\vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o}$$

The Attempt at a Solution

When I compute the dot product of gradient operator with the E-field I get zero since the only "term" in the factor is in the y direction, but it also does not have any variation with y so is the charge density in this region of space just zero?

 

[Dick]

Homework Statement

I have a function for an E-field $$E(x,y,z,t)=E_o\cos(k(x-ct))\hat j$$ and I need to find the charge density...

Homework Equations

$$\vec \nabla \cdot\vec E=\frac{\rho}{\epsilon_o}$$

The Attempt at a Solution

When I compute the dot product of gradient operator with the E-field I get zero since the only "term" in the factor is in the y direction, but it also does not have any variation with y so is the charge density in this region of space just zero?

I would agree with that.