A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of 2, and the cylinder has a net charge per unit length of 21. From this information, use Gauss's law to find the following. (Use any variable or symbol stat above along with the following as necessary: o and m.) (a) the charge per unit length on the inner surface of the cylinder Ainner - (b) the charge per unit length on the outer surface of the cylinder Aouter- (c) the electric field outside the cylinder a distance r from the axis magnitude E- direction --Select-- V

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**Title: Application of Gauss's Law to a Cylindrical System**

**Problem Statement:**
A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ.

Using this information, apply Gauss's law to find the following:

(a) **Charge per Unit Length on the Inner Surface of the Cylinder:**
   - \(\lambda_{\text{inner}} = \) [ ]

(b) **Charge per Unit Length on the Outer Surface of the Cylinder:**
   - \(\lambda_{\text{outer}} = \) [ ]

(c) **Electric Field Outside the Cylinder a Distance \( r \) from the Axis:**
   - Magnitude \( E = \) [ ]
   - Direction: [Select]

**Instructions:** Use any necessary variable or symbol stated above. Utilize constants such as \( \varepsilon_0 \) and \(\pi\) for calculation purposes. 

**Diagram Explanation:**  
Though not illustrated here, imagine a cross-section showing:
- A central wire with a uniform linear charge density \(\lambda\).
- An encompassing cylindrical shell with a net charge per unit length of 2λ.
- Indicating surfaces for charges and regions for evaluating the electric field. 

**Topics Covered:**
- Gauss's Law
- Electric Fields
- Cylindrical Symmetry
- Charge Distribution
Transcribed Image Text:**Title: Application of Gauss's Law to a Cylindrical System** **Problem Statement:** A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire has a charge per unit length of λ, and the cylinder has a net charge per unit length of 2λ. Using this information, apply Gauss's law to find the following: (a) **Charge per Unit Length on the Inner Surface of the Cylinder:** - \(\lambda_{\text{inner}} = \) [ ] (b) **Charge per Unit Length on the Outer Surface of the Cylinder:** - \(\lambda_{\text{outer}} = \) [ ] (c) **Electric Field Outside the Cylinder a Distance \( r \) from the Axis:** - Magnitude \( E = \) [ ] - Direction: [Select] **Instructions:** Use any necessary variable or symbol stated above. Utilize constants such as \( \varepsilon_0 \) and \(\pi\) for calculation purposes. **Diagram Explanation:** Though not illustrated here, imagine a cross-section showing: - A central wire with a uniform linear charge density \(\lambda\). - An encompassing cylindrical shell with a net charge per unit length of 2λ. - Indicating surfaces for charges and regions for evaluating the electric field. **Topics Covered:** - Gauss's Law - Electric Fields - Cylindrical Symmetry - Charge Distribution
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