A uniformly charged conducting sphere of 1.3m diameter has a surface charge density of 9.4 uC/m². (a) Find the net charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? (a) Number Units (b) Number i Units
A uniformly charged conducting sphere of 1.3m diameter has a surface charge density of 9.4 uC/m². (a) Find the net charge on the sphere. (b) What is the total electric flux leaving the surface of the sphere? (a) Number Units (b) Number i Units
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 Description:**
A uniformly charged conducting sphere of 1.3 m diameter has a surface charge density of 9.4 μC/m².
**Questions:**
(a) Find the net charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?
**Solution Inputs:**
(a)
- Number: [Input box]
- Units: [Dropdown menu]
(b)
- Number: [Input box]
- Units: [Dropdown menu]
---
**Steps to Solve the Problem:**
1. **Calculate the Net Charge on the Sphere:**
Given:
- Diameter of the sphere, \(d = 1.3 \, \text{m}\)
- Surface charge density, \(\sigma = 9.4 \, \mu\text{C/m}^2\)
- Radius of the sphere, \(r = \frac{d}{2} = \frac{1.3 \, \text{m}}{2}\)
Use the formula for the surface area of a sphere, \(A = 4 \pi r^2\), to find the surface area.
Net charge \(Q\) is calculated using \(Q = \sigma \times A\).
2. **Calculate the Total Electric Flux:**
According to Gauss's law, the total electric flux \(\Phi\) leaving a closed surface is related to the net charge \(Q\) by:
\(\Phi = \frac{Q}{\epsilon_0}\),
where,
- \(\epsilon_0\) is the permittivity of free space (\(8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2\)).
---
**Interactive Elements:**
The interactive solution inputs allow students to enter numerical values and select appropriate units. This enhances conceptual understanding and application of electric charge and flux calculations in electrostatic contexts.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe462800b-ac16-4590-bafb-82d68c005ec5%2F9578c8cf-7e2f-4199-99a6-8147ee0a3e95%2Fgl61x2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Description:**
A uniformly charged conducting sphere of 1.3 m diameter has a surface charge density of 9.4 μC/m².
**Questions:**
(a) Find the net charge on the sphere.
(b) What is the total electric flux leaving the surface of the sphere?
**Solution Inputs:**
(a)
- Number: [Input box]
- Units: [Dropdown menu]
(b)
- Number: [Input box]
- Units: [Dropdown menu]
---
**Steps to Solve the Problem:**
1. **Calculate the Net Charge on the Sphere:**
Given:
- Diameter of the sphere, \(d = 1.3 \, \text{m}\)
- Surface charge density, \(\sigma = 9.4 \, \mu\text{C/m}^2\)
- Radius of the sphere, \(r = \frac{d}{2} = \frac{1.3 \, \text{m}}{2}\)
Use the formula for the surface area of a sphere, \(A = 4 \pi r^2\), to find the surface area.
Net charge \(Q\) is calculated using \(Q = \sigma \times A\).
2. **Calculate the Total Electric Flux:**
According to Gauss's law, the total electric flux \(\Phi\) leaving a closed surface is related to the net charge \(Q\) by:
\(\Phi = \frac{Q}{\epsilon_0}\),
where,
- \(\epsilon_0\) is the permittivity of free space (\(8.85 \times 10^{-12} \, \text{C}^2/\text{Nm}^2\)).
---
**Interactive Elements:**
The interactive solution inputs allow students to enter numerical values and select appropriate units. This enhances conceptual understanding and application of electric charge and flux calculations in electrostatic contexts.
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