Engineering Electromagnetics
9th Edition
ISBN: 9780078028151
Author: Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher: Mcgraw-hill Education,
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Chapter 4, Problem 4.12P
To determine
(a)
The potential at any point, when
To determine
(b)
The potential at any point, when
To determine
(c)
The potential at any point, when
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Chapter 4 Solutions
Engineering Electromagnetics
Ch. 4 - Given E = Exax + Eyay + Ez3z V/m, where EX, Ey,...Ch. 4 - A positive point charge of magnitude q1 lies at...Ch. 4 - Given E=Epap+Ea+Ez+azV/m, where Ep, E and E2 are...Ch. 4 - An electric field in free space is given by...Ch. 4 - Consider the vector field G = (A/p) aa where A is...Ch. 4 - A electric field in free space is given as...Ch. 4 - Prob. 4.7PCh. 4 - Given E=-xax+yay,(a) find the work involved in...Ch. 4 - An electric field intensity in spherical...Ch. 4 - A sphere of radios a carries a surface density of...
Ch. 4 - At large distances from a dipole antenna (to be...Ch. 4 - Prob. 4.12PCh. 4 - Thee identical point charges of 4 pC each are...Ch. 4 - Given the electric field E=(y+1)ax+(x1)ay+2az find...Ch. 4 - Two uniform lines, 8 nC/m, are located at x=1, z=2...Ch. 4 - A spherically symmetric charge distribution in...Ch. 4 - Uniform surface charge densities of 6 and 2 nC/m2...Ch. 4 - Find the potential at the origin produced by a...Ch. 4 - Volume charge density is given as pv=poer/C/m3,...Ch. 4 - En a certain medium, the electric potential is...Ch. 4 - Prob. 4.21PCh. 4 - A Line charge of infinite length lies along the z...Ch. 4 - Prob. 4.23PCh. 4 - A certain spherically symmetric charge...Ch. 4 - Consider an electric field intensity in free space...Ch. 4 - Let us assume that we have a very thin, square,...Ch. 4 - By performing an appropriate Line integral from...Ch. 4 - Prob. 4.28PCh. 4 - A dipole having a moment P=3ax-5ay+10aznC.m is...Ch. 4 - Prob. 4.30PCh. 4 - A potential field in free space is expressed as...Ch. 4 - Prob. 4.32PCh. 4 - Prob. 4.33PCh. 4 - A sphere of radius a contains volume charge of...Ch. 4 - Four 0.8 nC point charge are located in free space...Ch. 4 - Surface charge of uniform density ps lies on a...
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- In free space, there are 2 concentric spherical surfaces with radii a and b. There is a constant volume charge density between 2 surfaces such that: ρ= { 0; ρb [ ? ?3 ] a) Find the electric potential everywhere using Poisson’s equation. b) Find the electric field vector everywhere using Poisson’s equationarrow_forward1.A charge QM is at point Mx= 16 My= -12 Mz = 20, and a charge QN is at N(-18, 3, 7) in free space. If distances are given in cm,solve for: A. RMN B. RMN C. Determine the vector force exerted on QM by QN if the permittivity of free space is equal to 10-9 / 36π. If the charges are -25µC and 40µC respectively.arrow_forwardIn the 0<r<1mm cubic region, it is given as ρ_v=2e^(-100r) nC/m^3. In other places, the charge density is given as 0.a) Find the total charge inside the spherical surface r=1mm.b) Calculate the expression Dr on the r=1mm surface using Gauss's law.arrow_forward
- Given a charge distribution with density ρv = 5r C/m3 in spherical coordinates, use Gauss Law to find D.arrow_forwardQ1. In free space, there are 2 concentric spherical surfaces with radii a and b. There is a constant volume charge density between 2 surfaces such that:a) Find the electric potential everywhere using Poisson’s equation. b) Find the electric field vector everywhere using Poisson’s equation.arrow_forwardQ1. Uniform line charges of 40nC/m lie along the entire extent of the three coordinate axes.Assuming free space condition, find E̅at P( -2,1, 2). Q2. The work is defined by the equation: ? = 2 cos ? − 4?2?2 . Determine the curl of thegradient of the work and comment on the result.arrow_forward
- Spherical surfaces at r = 1, 3, and 6 m carry uniform surface charge densities of 20 nC/m2, −4 nC/m2, and ρS0, respectively. Find D at r = 0.5, 2, 5, and 7 m.arrow_forwardWithin the cylinder ρ = 2, 0 < z < 1, the potential is given by V = 100+50ρ+150ρsin ϕ V. Find V, E, D, and ρv at P(1,60°,0.5) in free space.arrow_forwardA closed surface is defined in cylindrical coordinates by: 2 < ρ < 5, 0.07 π≤ϕ≤π7 and 1.93≤ z ≤0. Find the the surface area of the spherearrow_forward
- A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. 1. Use Gauss's law to find an expression for the magnitude of the electric field strength E inside the sphere, r≤R, and r>- (more or equal) in terms of Q and R.arrow_forwardA thin circular ring of radius a=5 mm lies in the x-y plane and is centered at the origin as shown in Figure . Assume that the ring is in air and carries a uniform line charge density The electric potential at point P(0,0,4) cm is equal toarrow_forwardGiven a scalar field V=2xy-yz+xz i.Find the vector representing the direction and magnitude of the maximum rate of increase of V at pointp(2,-1,0) and ii. find the rate of increase of V at point pin the direction toward pointQ(0,2.6)arrow_forward
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