Please help with number 11 **Educational Content: Electric Fields and Resistive Rods**In this exercise, we explore a rod divided into three sections with differing radii, subjected to an electric field. The aim is to determine the radii of sections 1 and 2.**Description:**- **Figure (a):** This graph plots the magnitude $ E(x) $ of the electric fields along a resistive rod, as established by a battery. The rod is segmented into three parts (labeled 1, 2, and 3) and spans a total length $ L = 9.00 $ mm. - The vertical axis represents the electric field $ E $ in units of $ 10^{3} $ V/m, with a scale defined by $ E_s = 5.20 \times 10^{3} $ V/m. - The horizontal axis shows the position $ x $ along the rod in millimeters. - Sections 1, 2, and 3 are visually distinct by breaks in the electric field values: - Section 1 spans from 0 to 3 mm. - Section 2 spans from 3 to 6 mm. - Section 3 spans from 6 to 9 mm and is known to have a radius of 2.04 mm.- **Figure (b):** A schematic diagram depicting a battery connected to one end of the rod, with the other end marked $ x = L $. Note that this diagram does not visually represent the differences in radii for sections 1, 2, and 3.**Objective:**Determine the radius of:- (a) Section 1- (b) Section 2Given the radius of section 3, use the relative magnitudes of the electric fields to deduce the radii of the unknown sections based on their resistances. Use the provided inputs in the form fields for numerical answers and select appropriate units for your calculations.

Answered: Figure (a) gives the magnitude E(x) of…

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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Please help with number 11

**Educational Content: Electric Fields and Resistive Rods**

In this exercise, we explore a rod divided into three sections with differing radii, subjected to an electric field. The aim is to determine the radii of sections 1 and 2.

**Description:**

- **Figure (a):** This graph plots the magnitude $ E(x) $ of the electric fields along a resistive rod, as established by a battery. The rod is segmented into three parts (labeled 1, 2, and 3) and spans a total length $ L = 9.00 $ mm.
- The vertical axis represents the electric field $ E $ in units of $ 10^{3} $ V/m, with a scale defined by $ E_s = 5.20 \times 10^{3} $ V/m.
- The horizontal axis shows the position $ x $ along the rod in millimeters.
- Sections 1, 2, and 3 are visually distinct by breaks in the electric field values:
- Section 1 spans from 0 to 3 mm.
- Section 2 spans from 3 to 6 mm.
- Section 3 spans from 6 to 9 mm and is known to have a radius of 2.04 mm.

- **Figure (b):** A schematic diagram depicting a battery connected to one end of the rod, with the other end marked $ x = L $. Note that this diagram does not visually represent the differences in radii for sections 1, 2, and 3.

**Objective:**

Determine the radius of:
- (a) Section 1
- (b) Section 2

Given the radius of section 3, use the relative magnitudes of the electric fields to deduce the radii of the unknown sections based on their resistances. Use the provided inputs in the form fields for numerical answers and select appropriate units for your calculations.

Expert Solution

Step 1

Since the pieces are connected in series, the current will be the same. Also, the resistivity will be the same because the sections have the same material.

Write the expression for the current density.

$\begin{array}{l} J = \frac{I}{A} = \frac{E}{ρ} \\ A E = I ρ \\ A E = c \\ A_{1} E_{1} = A_{2} E_{2} = A_{3} E_{3} \end{array}$

Here, I is the current, A is the cross-sectional area, E is the electric field, ρ is the density, and c is constant.

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