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A rod of length L is lying on x-axis with left end at the origin and has a non-uniformly linear charge density of 1 = 5x. find the electric potential V at A(-4, 0) Hint: dv= Kdt , dg- 2dx d2 = 1dx (-4,0) + + + + A

A rod of length L is lying on x-axis with left end at the origin and has a non-uniformly linear charge density of 1 = 5x. find the electric potential V at A(-4, 0) Hint: dv= Kdt , dg- 2dx d2 = 1dx (-4,0) + + + + A

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** A rod of length \( L \) is lying on the x-axis with its left end at the origin and has a non-uniformly linear charge density of \( \lambda = 5x \). Find the electric potential \( V \) at point A \((-4, 0)\). **Hint:** \[ dV = \frac{k \, dQ}{r} \] \[ dQ = \lambda \, dx \] **Diagram Explanation:** In the diagram, the x-axis is shown with a rod of length \( L \) lying on it. The rod has a positive charge distributed along its length, and the linear charge density is non-uniform, given as \( \lambda = 5x \). - The point A \((-4, 0)\) is marked on the x-axis, which is the point where the electric potential is to be calculated. - The distance from each infinitesimal element of the rod to point A is represented as \( r \). - An elemental section of the rod at a distance \( x \) from the origin is considered for the integration, showing its contribution to the electric potential at point A. The task involves using the hint equations to compute the potential by integrating over the length of the rod from 0 to \( L \).
Transcribed Image Text:**Problem Statement:** A rod of length \( L \) is lying on the x-axis with its left end at the origin and has a non-uniformly linear charge density of \( \lambda = 5x \). Find the electric potential \( V \) at point A \((-4, 0)\). **Hint:** \[ dV = \frac{k \, dQ}{r} \] \[ dQ = \lambda \, dx \] **Diagram Explanation:** In the diagram, the x-axis is shown with a rod of length \( L \) lying on it. The rod has a positive charge distributed along its length, and the linear charge density is non-uniform, given as \( \lambda = 5x \). - The point A \((-4, 0)\) is marked on the x-axis, which is the point where the electric potential is to be calculated. - The distance from each infinitesimal element of the rod to point A is represented as \( r \). - An elemental section of the rod at a distance \( x \) from the origin is considered for the integration, showing its contribution to the electric potential at point A. The task involves using the hint equations to compute the potential by integrating over the length of the rod from 0 to \( L \).
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