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4. A hollow very long non-conducting cylindrical shell has inner radius R1 and outer radius R2. A very thin wire with linear charge density A lies at the center of the shell. The shell carries a cylindrically symmetric charge density p = br for R1

4. A hollow very long non-conducting cylindrical shell has inner radius R1 and outer radius R2. A very thin wire with linear charge density A lies at the center of the shell. The shell carries a cylindrically symmetric charge density p = br for R1

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The question is attached to this post. This problem is noncalculator question and please give full reasoning to the answer. Please answer question 5, not 4. I attached question 4 as well because, for question 5, we need question 4. 

### Problem 4: A hollow very long non-conducting cylindrical shell has inner radius \(R_1\) and outer radius \(R_2\). A very thin wire with linear charge density \(\lambda_l\) lies at the center of the shell. The shell carries a cylindrically symmetric charge density \(\rho = br\) for \(R_1 < r < R_2\) that increases linearly with radius (but doesn’t change along the length), where \(b\) is a constant of proportionality. **Draw and label** a Gaussian surface and use Gauss's Law to find the radial electric field in the region \(r < R_1\). You may take the positive direction as outward. **Equation:** \[ 4. \, E = \, \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \] **Diagram Explanation:** The diagram illustrates a hollow cylindrical shell with a marked inner radius \(R_1\) and an outer radius \(R_2\). It depicts a thin wire at the center, along with dashed lines to indicate the region of the Gaussian surface for consideration. ### Problem 5: For the same cylindrical shell as in the previous problem, **draw and label** a Gaussian surface and use Gauss's Law to find the radial electric field in the region \(R_1 < r < R_2\). You may take the positive direction as outward. *(Hint: I adapted this problem from #20 in the first online homework assignment. Use your work on that problem to guide your work for this problem.)* The diagram for Problem 5 is identical to that of Problem 4, highlighting the shell and central wire, with the Gaussian surface region marked as previously described.
Transcribed Image Text:### Problem 4: A hollow very long non-conducting cylindrical shell has inner radius \(R_1\) and outer radius \(R_2\). A very thin wire with linear charge density \(\lambda_l\) lies at the center of the shell. The shell carries a cylindrically symmetric charge density \(\rho = br\) for \(R_1 < r < R_2\) that increases linearly with radius (but doesn’t change along the length), where \(b\) is a constant of proportionality. **Draw and label** a Gaussian surface and use Gauss's Law to find the radial electric field in the region \(r < R_1\). You may take the positive direction as outward. **Equation:** \[ 4. \, E = \, \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad} \] **Diagram Explanation:** The diagram illustrates a hollow cylindrical shell with a marked inner radius \(R_1\) and an outer radius \(R_2\). It depicts a thin wire at the center, along with dashed lines to indicate the region of the Gaussian surface for consideration. ### Problem 5: For the same cylindrical shell as in the previous problem, **draw and label** a Gaussian surface and use Gauss's Law to find the radial electric field in the region \(R_1 < r < R_2\). You may take the positive direction as outward. *(Hint: I adapted this problem from #20 in the first online homework assignment. Use your work on that problem to guide your work for this problem.)* The diagram for Problem 5 is identical to that of Problem 4, highlighting the shell and central wire, with the Gaussian surface region marked as previously described.
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