### Example Problem for Applying Gauss's Law#### InstructionsIn each figure, the dashed circle represents the cross section of a closed Gaussian surface.#### Diagram DescriptionIn the provided diagram:- Several point charges are shown, both inside and outside the dashed circle (representing a Gaussian surface): - Inside the circle: - +2.0 mC (milliCoulombs) - +3.0 mC - + an unknown charge (labeled as $q = ?$) - Outside the circle: - +2.0 mC - -3.0 mC (Note: mC is milliCoulombs, a unit for measuring electric charge)#### Problem StatementThe net electric flux passing through the Gaussian surface is given as $+3.9 \times 10^8 \, \text{N} \cdot \text{m}^2/\text{C}$. Question: What is the value of the unknown charge within the Gaussian surface?---### SolutionTo find the unknown charge ($ q $), we use Gauss's Law which states:\[ \Phi_E = \frac{q_{\text{enc}}}{\epsilon_0} \]where:- $\Phi_E$ is the electric flux through the surface.- $q_{\text{enc}}$ is the total charge enclosed within the Gaussian surface.- $\epsilon_0$ is the permittivity of free space, $ \epsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2/\text{N} \cdot \text{m}^2 $.Given data:- $\Phi_E = +3.9 \times 10^8 \, \text{N} \cdot \text{m}^2 / \text{C} $Calculate the total enclosed charge ($ q_{\text{enc}} $):\[ q_{\text{enc}} = \Phi_E \cdot \epsilon_0 \]\[ q_{\text{enc}} = (3.9 \times 10^8 \, \text{N} \cdot \text{m}^2/\text{C}) \times (8.85 \times 10^{-12} \, \text{C}^2/\text

Gauss law states that net electric flux through any closed surface is equal to the net charge…

In each figure, the dashed circle is the cross section of a closed Gaussian surface. +2.0 mC +2.0 mC q=? +3.0 mC -3.0 mC The net electric flux passing through the Gaussian surface is +3.9 × 108 N · m²/C. What is the value of the unknown charge?

In each figure, the dashed circle is the cross section of a closed Gaussian surface. +2.0 mC +2.0 mC q=? +3.0 mC -3.0 mC The net electric flux passing through the Gaussian surface is +3.9 × 108 N · m²/C. What is the value of the unknown charge?

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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