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A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. You may assume that the potential is defined to be zero at a distance of 1 meter from the center of the system and that the length Lis much longer than the radius R. (Figure 1) Figure 1 of 1

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. You may assume that the potential is defined to be zero at a distance of 1 meter from the center of the system and that the length Lis much longer than the radius R. (Figure 1) Figure 1 of 1

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### Description of the System: A hollow cylindrical shell of length \( L \) and radius \( R \) has charge \( Q \) uniformly distributed along its length. You may assume that the potential is defined to be zero at a distance of 1 meter from the center of the system and that the length \( L \) is much longer than the radius \( R \). ### Explanation of the Figure: The figure illustrates a hollow cylindrical shell with three arrows pointing outward from the top surface, indicating the direction of the electric field extending radially outward from the surface. The cylindrical shape is shown with straight vertical lines representing its sides and a circular curve at the top denoting its open circular face. The arrows suggest a symmetrical distribution of charge along the length of the cylinder, consistent with a uniform electric field. The diagram helps visualize the setup described in the text, which is often used in electrostatics to discuss potentials and fields around charged cylindrical objects.
Transcribed Image Text:### Description of the System: A hollow cylindrical shell of length \( L \) and radius \( R \) has charge \( Q \) uniformly distributed along its length. You may assume that the potential is defined to be zero at a distance of 1 meter from the center of the system and that the length \( L \) is much longer than the radius \( R \). ### Explanation of the Figure: The figure illustrates a hollow cylindrical shell with three arrows pointing outward from the top surface, indicating the direction of the electric field extending radially outward from the surface. The cylindrical shape is shown with straight vertical lines representing its sides and a circular curve at the top denoting its open circular face. The arrows suggest a symmetrical distribution of charge along the length of the cylinder, consistent with a uniform electric field. The diagram helps visualize the setup described in the text, which is often used in electrostatics to discuss potentials and fields around charged cylindrical objects.
**Question:** What is the electric potential at the center of the cylinder? \((r = 0)\) Express your answer in terms of variables \(Q, L, r,\) and \(R\). Combine all numerical values together into one multiplier. - View Available Hint(s) **Input Box:** \[ V_0 = \] The interface includes tools for formatting such as subscript/superscript, symbols, undo/redo functions, and an input box for entering the solution.
Transcribed Image Text:**Question:** What is the electric potential at the center of the cylinder? \((r = 0)\) Express your answer in terms of variables \(Q, L, r,\) and \(R\). Combine all numerical values together into one multiplier. - View Available Hint(s) **Input Box:** \[ V_0 = \] The interface includes tools for formatting such as subscript/superscript, symbols, undo/redo functions, and an input box for entering the solution.
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