Explanation Given: Radius =3.00 mm Charge =2.00 C per meter length of wire. Range is 0 ≤ ρ ≤ 9 mm Calculation: Write the expression for volume charge density. ρ ν = 2 π a 2 Substitute 3 × 10 − 3 m for a . ρ ν = 2 π a 2 = 2 π ( 3 × 10 − 3 ) 2 = 70 , 735.53 C/m 3 Write the expression for charge enclosed. Q e n c = ∮ D ⋅ d S = ∫ D ρ a ρ ⋅ ρ d ϕ d Z a ρ = 2 π ρ L D ρ Here, L is the length of the wire, ρ is the radius of the wire. Case 1: When radius ρ is less than the radius a, the charge enclosed Q e n c can be expressed as follows: Q e n c = ∫ ρ ν d ν = ρ ν ∫ 0 ρ ρ d ρ ∫ 0 2 π d ϕ ∫ 0 L d z = ρ ν ρ 2 π L Express the divergence D ρ D ρ = ρ ν ρ 2 π L 2 π ρ L = ρ ν 2 ρ for ρ ≤ a Case 2: When radius ρ is greater than the radius a, the charge enclosed Q e n c can be expressed as follows: Q e n c = ρ ν a 2 π L Express the divergence D ρ

Fundamentals of Electromagnetics with Engineering Applications

5th Edition

ISBN: 9780471263555

Author: Stuart M. Wentworth

Publisher: John Wiley & Sons

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Question

Chapter 2, Problem 2.31P

To determine

To plot: The electric flux density versus radial distance

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Chapter 2, Problem 2.30P

Chapter 2, Problem 2.33P

Chapter 2 Solutions

Fundamentals of Electromagnetics with Engineering Applications

Ch. 2 - Given P(4, 2, 1) and APQ=2ax+4ay+6az, find the...Ch. 2 - Prob. 2.2P Ch. 2 - Prob. 2.3P Ch. 2 - Suppose Q1(0.0,-3.0m,0.0)=4.0nC,...Ch. 2 - Prob. 2.5P Ch. 2 - Suppose 10.0nC point charges are located on the...Ch. 2 - Four 1.00nC point charges are located at...Ch. 2 - A 20.0nC point charge exists at...Ch. 2 - Prob. 2.9P Ch. 2 - Convert the following points from Cartesian to...

Ch. 2 - Prob. 2.11P Ch. 2 - Prob. 2.12P Ch. 2 - Prob. 2.13P Ch. 2 - A 20.0â€“cmâ€“long section of copper pipe has a...Ch. 2 - A line charge with charge density 2.00nC/m exists...Ch. 2 - You are given two zâ€“directed line charges of...Ch. 2 - Suppose you have a segment of line charge of...Ch. 2 - A segment of line charge L=10.nC/m exists on the...Ch. 2 - In free space, there is a point charge Q=8.0nC at...Ch. 2 - Prob. 2.20P Ch. 2 - Sketch the following surfaces and find the total...Ch. 2 - Consider a circular disk in the xâ€“y plane of...Ch. 2 - Suppose a ribbon of charge with density S exists...Ch. 2 - Sketch the following volumes and find the total...Ch. 2 - You have a cylinder of 4.00â€“in diameter and...Ch. 2 - Consider a rectangular volume with...Ch. 2 - Prob. 2.27P Ch. 2 - Prob. 2.28P Ch. 2 - Given D=2a+sinazC/m2, find the electric flux...Ch. 2 - Suppose the electric flux density is given by...Ch. 2 - Prob. 2.31P Ch. 2 - A cylindrical pipe with a 1.00â€“cm wall thickness...Ch. 2 - Prob. 2.34P Ch. 2 - Prob. 2.35P Ch. 2 - A thickâ€“walled spherical shell, with inner...Ch. 2 - Prob. 2.37P Ch. 2 - Determine the charge density at the point...Ch. 2 - Given D=3ax+2xyay+8x2y3azC/m2, (a) determine the...Ch. 2 - Suppose D=6cosaC/m2. (a) Determine the charge...Ch. 2 - Suppose D=r2sinar+sincosaC/m2. (a) Determine the...Ch. 2 - Prob. 2.42P Ch. 2 - A surface is defined by the function 2x+4y21nz=12....Ch. 2 - For the following potential distributions, use the...Ch. 2 - A 100nC point charge is located at the origin. (a)...Ch. 2 - Prob. 2.46P Ch. 2 - Prob. 2.47P Ch. 2 - Prob. 2.48P Ch. 2 - Suppose a 6.0â€“mâ€“diameter ring with charge...Ch. 2 - Prob. 2.50P Ch. 2 - Prob. 2.51P Ch. 2 - The typical length of each piece of jumper wire on...Ch. 2 - A 150â€“m length of AWGâ€“22 (0.644 mm diameter)...Ch. 2 - Determine an expression for the power dissipated...Ch. 2 - Find the resistance per unit length of a stainless...Ch. 2 - A nickel wire of diameter 5.0 mm is surrounded by...Ch. 2 - Prob. 2.57P Ch. 2 - A 20nC point charge at the origin is embedded in...Ch. 2 - Suppose the force is very carefully measured...Ch. 2 - The potential field in a material with r=10.2 is...Ch. 2 - In a mineral oil dielectric, with breakdown...Ch. 2 - Prob. 2.62P Ch. 2 - For z0,r1=9.0 and for z0,r2=4.0. If E1 makes a 300...Ch. 2 - Prob. 2.64P Ch. 2 - Consider a dielectricâ€“dielectric chargeâ€“free...Ch. 2 - A 1.0â€“cmâ€“diameter conductor is sheathed with a...Ch. 2 - Prob. 2.67P Ch. 2 - For a coaxial cable of inner conductor radius a...Ch. 2 - Prob. 2.69P Ch. 2 - Prob. 2.70P Ch. 2 - A parallelâ€“plate capacitor with a 1.0m2 surface...Ch. 2 - Prob. 2.72P Ch. 2 - Prob. 2.73P Ch. 2 - Given E=5xyax+3zaZV/m, find the electrostatic...Ch. 2 - Suppose a coaxial capacitor with inner radius 1.0...

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