### Problem StatementA charge of uniform density (29 nC/m) is distributed along the x-axis from the origin to the point \( x = 18.3 \, \text{m} \). What is the electric potential (relative to zero at infinity) at a point, \( x = 73.6 \, \text{m} \), on the x-axis?#### ExplanationTo solve this problem, it's essential to understand how electric potential is calculated for a distributed charge along a segment of the x-axis. The problem involves:1. **Uniform Charge Density** (\(\lambda = 29 \, \text{nC/m}\)): This is the charge per unit length.2. **Distribution Range**: The charge is distributed from \( x = 0 \) to \( x = 18.3 \, \text{m} \).3. **Observation Point**: The electric potential needs to be found at \( x = 73.6 \, \text{m} \).In solving this, you would integrate the contributions to the electric potential from each infinitesimal element of the charge distribution along the given range. The contributions would depend on the distance of these elements from the observation point.If diagrams or graphs were present, they would likely illustrate:- The linear charge distribution along the x-axis from 0 to 18.3 meters.- The position of the observation point at \( x = 73.6 \, \text{m} \).- The variable distance between an infinitesimal element located at a general position \( x' \) and the observation point.This approach helps visualize how the integral setup would account for the distance from each charge element to the point of interest.

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A charge of uniform density (29 nC/m) is distributed along the x axis from the origin to the point x = 18.3 m. What is the electric potential (relative to zero at infinity) at a point, X = 73.6 m, on the x axis?

A charge of uniform density (29 nC/m) is distributed along the x axis from the origin to the point x = 18.3 m. What is the electric potential (relative to zero at infinity) at a point, X = 73.6 m, on the x axis?

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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Concept explainers

Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

Question

### Problem Statement

A charge of uniform density (29 nC/m) is distributed along the x-axis from the origin to the point \( x = 18.3 \, \text{m} \). What is the electric potential (relative to zero at infinity) at a point, \( x = 73.6 \, \text{m} \), on the x-axis?

#### Explanation

To solve this problem, it's essential to understand how electric potential is calculated for a distributed charge along a segment of the x-axis. The problem involves:

1. **Uniform Charge Density** (\(\lambda = 29 \, \text{nC/m}\)): This is the charge per unit length.
2. **Distribution Range**: The charge is distributed from \( x = 0 \) to \( x = 18.3 \, \text{m} \).
3. **Observation Point**: The electric potential needs to be found at \( x = 73.6 \, \text{m} \).

In solving this, you would integrate the contributions to the electric potential from each infinitesimal element of the charge distribution along the given range. The contributions would depend on the distance of these elements from the observation point.

If diagrams or graphs were present, they would likely illustrate:

- The linear charge distribution along the x-axis from 0 to 18.3 meters.
- The position of the observation point at \( x = 73.6 \, \text{m} \).
- The variable distance between an infinitesimal element located at a general position \( x' \) and the observation point.

This approach helps visualize how the integral setup would account for the distance from each charge element to the point of interest.

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