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What is the electric field outside the cylinder (r > R)? Give your answer in terms of the variables A, r, and R. Combine all numerical values together into one numerical multiplier. ΑΣφ E outside for r> R Submit Request Answer Part B What is the potential difference between a point at radius r and the surface of the cylinder? Give your answer in terms of the variables A, r, and R. Combine all numerical values together into one numerical multiplier. ΑΣφ ? AV =

What is the electric field outside the cylinder (r > R)? Give your answer in terms of the variables A, r, and R. Combine all numerical values together into one numerical multiplier. ΑΣφ E outside for r> R Submit Request Answer Part B What is the potential difference between a point at radius r and the surface of the cylinder? Give your answer in terms of the variables A, r, and R. Combine all numerical values together into one numerical multiplier. ΑΣφ ? AV =

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## Electric Field and Potential Difference in Cylindrical Geometry ### Problem Statement #### Part A **Question:** What is the electric field outside the cylinder (\( r > R \))? **Instructions:** Give your answer in terms of the variables \(\lambda\), \(r\), and \(R\). Combine all numerical values together into one numerical multiplier. **Equation:** \[ E_{\text{outside}} = \_\_\_\_ \quad \text{for } r > R \] **Submit:** [Submit Answer] **Help:** [Request Answer] --- #### Part B **Question:** What is the potential difference between a point at radius \( r \) and the surface of the cylinder? **Instructions:** Give your answer in terms of the variables \(\lambda\), \(r\), and \(R\). Combine all numerical values together into one numerical multiplier. **Equation:** \[ \Delta V = \_\_\_\_ \] **Submit:** [Submit Answer] **Help:** [Request Answer] ### Diagram/Tool Explanation Each part includes a text box for inputting equations. Users can access mathematical symbols and formatting tools via a toolbar to help input their solutions. The interface provides submission buttons to evaluate the student's solution and request help if needed.
Transcribed Image Text:## Electric Field and Potential Difference in Cylindrical Geometry ### Problem Statement #### Part A **Question:** What is the electric field outside the cylinder (\( r > R \))? **Instructions:** Give your answer in terms of the variables \(\lambda\), \(r\), and \(R\). Combine all numerical values together into one numerical multiplier. **Equation:** \[ E_{\text{outside}} = \_\_\_\_ \quad \text{for } r > R \] **Submit:** [Submit Answer] **Help:** [Request Answer] --- #### Part B **Question:** What is the potential difference between a point at radius \( r \) and the surface of the cylinder? **Instructions:** Give your answer in terms of the variables \(\lambda\), \(r\), and \(R\). Combine all numerical values together into one numerical multiplier. **Equation:** \[ \Delta V = \_\_\_\_ \] **Submit:** [Submit Answer] **Help:** [Request Answer] ### Diagram/Tool Explanation Each part includes a text box for inputting equations. Users can access mathematical symbols and formatting tools via a toolbar to help input their solutions. The interface provides submission buttons to evaluate the student's solution and request help if needed.
**Text Transcription:** An infinitely long cylinder of radius \( R \) has linear charge density \( \lambda \). (Figure 1) **Figure Description:** The diagram shows an infinitely long cylinder with arrows pointing along its length, indicating its infinite nature. The cylinder is labeled as "Infinite Cylinder." The linear charge density is represented by the symbol \( \lambda \), placed in the middle of the cylinder. The radius of the cylinder is denoted as \( R \). This diagram helps illustrate the concept of linear charge density along the length of a cylindrical structure, useful in understanding electric fields around charged cylinders in physics.
Transcribed Image Text:**Text Transcription:** An infinitely long cylinder of radius \( R \) has linear charge density \( \lambda \). (Figure 1) **Figure Description:** The diagram shows an infinitely long cylinder with arrows pointing along its length, indicating its infinite nature. The cylinder is labeled as "Infinite Cylinder." The linear charge density is represented by the symbol \( \lambda \), placed in the middle of the cylinder. The radius of the cylinder is denoted as \( R \). This diagram helps illustrate the concept of linear charge density along the length of a cylindrical structure, useful in understanding electric fields around charged cylinders in physics.
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Step 1

Given,

An infinite long cylinder of radius R

Step 2

(A)

According to Gauss's law

∮E.da=Qenclosedε0

for r>R

∮E.da=∫0Rλdlε0E∮da=λ∫0Rdlε0E2πrl=λlε0Eoutside=λ2πrε0

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