Chapter 5.3, Problem 3bT

The Gaussian cylinder below encloses a portion of two identical large sheets. The charge density of the sheet on the left is $+{\sigma }_o$ : the charge density of the sheet on the right is $+2{\sigma }_o$ .

1. Find the net charge enclosed by the Gaussian cylinder in terms of ${\sigma }_o$ and any relevant dimensions.

2. Let $E_{\text{L}}\text{and}{E}_{\text{R}}$ be the magnitudes of the electric fields at the left and right end caps of the Gaussian cylinder respectively.

Is $E_{\text{L}}$ greater than, less than, or equal to $E_{\text{R}}$ ? Explain

3. Find the net flux through the Gaussian cylinder in terms of $E_{\text{L}}$ , $E_{\text{R}}$ , and any relevant dimensions.

4. Use Gauss’ law to find the electric field a distance $L_o$ to the right of the rightmost sheet.

Are your results consistent with the results you would obtain using superposition? Explain.