Lightning strikes a dielectric sphere of radius 20 mm for which &, = 2.5, σ = 5 x 10-6S/m and deposits uniformly a charge of 1 C. Determine the initial volume charge density and the volume charge density 2 us later.

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
icon
Related questions
Question
**Problem Statement:**

Lightning strikes a dielectric sphere of radius 20 mm for which \( \varepsilon_r = 2.5 \), \( \sigma = 5 \times 10^{-6} \) S/m and deposits uniformly a charge of 1 C. Determine the initial volume charge density and the volume charge density 2 μs later.

---

**Explanation:**

- **Dielectric Sphere Characteristics:**
  - Radius: 20 mm
  - Relative permittivity (\( \varepsilon_r \)): 2.5
  - Conductivity (\( \sigma \)): \( 5 \times 10^{-6} \) S/m

- **Charge Characteristics:**
  - Total charge deposited: 1 Coulomb
  - Initial volume charge density refers to the charge distributed within a given volume initially.
  - Volume charge density 2 microseconds later examines how the distribution changes with time due to the sphere's conductivity.

To solve the problem:
1. Calculate the initial volume charge density using the formula:
   \[
   \rho_0 = \frac{Q}{\frac{4}{3} \pi r^3}
   \]
   where \( Q \) is the total charge and \( r \) is the radius of the sphere.
   
2. Find how the volume charge density changes over time taking into account the conductivity \( \sigma \), which affects how charge redistributes over time. This question might involve exponential decay governed by material properties.

No diagrams or graphs are present in the image.
Transcribed Image Text:**Problem Statement:** Lightning strikes a dielectric sphere of radius 20 mm for which \( \varepsilon_r = 2.5 \), \( \sigma = 5 \times 10^{-6} \) S/m and deposits uniformly a charge of 1 C. Determine the initial volume charge density and the volume charge density 2 μs later. --- **Explanation:** - **Dielectric Sphere Characteristics:** - Radius: 20 mm - Relative permittivity (\( \varepsilon_r \)): 2.5 - Conductivity (\( \sigma \)): \( 5 \times 10^{-6} \) S/m - **Charge Characteristics:** - Total charge deposited: 1 Coulomb - Initial volume charge density refers to the charge distributed within a given volume initially. - Volume charge density 2 microseconds later examines how the distribution changes with time due to the sphere's conductivity. To solve the problem: 1. Calculate the initial volume charge density using the formula: \[ \rho_0 = \frac{Q}{\frac{4}{3} \pi r^3} \] where \( Q \) is the total charge and \( r \) is the radius of the sphere. 2. Find how the volume charge density changes over time taking into account the conductivity \( \sigma \), which affects how charge redistributes over time. This question might involve exponential decay governed by material properties. No diagrams or graphs are present in the image.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

Blurred answer
Knowledge Booster
Electric field
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,