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 4.10P
A sphere of radios a carries a surface density of pr0 C/m2. (a) Find the absolute potential at the sphere surface (b) A grounded connecting shell of radius b where b > a is now positioned around the charged sphere What is the potential at the inner sphere surface in this ease?
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A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c. The hollow sphere has no net charge.
(a) What is the charge on the inner surface of the hollow sphere? On the outer surface?
(b) Sketch the electric field lines of the system.
(c) Derive expressions for the electric field magnitude and for the electric potential interms of the distance r from the center for the regions r < a, a < r < b, b < r < c, and r > c. (Take the electric potential to vanish at r = ∞.)(d) Graph the magnitude of the electric field and the electric potential as a function of r from r = 0 to r = 2c.
Consider the surface charge distributed along the disk with an inner radius of 1m, an outer radius of 2m, and a charge density of 3[μC/m2] shown in the figure. Since the medium is empty space,
(a) Find the total charge on the disk.
(b) If a 2[μC] load is placed at point P1 10m above the axis of the load, find the force acting on this load.
Volume charge density is located in free space as ρν = 2e−100r nC/m3 for 0 < r < 3 mm, and ρν = 0 elsewhere.
Find the total charge enclosed by the spherical surface r = 2 mm.
By using Gauss’s law, calculate the value of Dr on the surface r = 2 mm.
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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- A volume charge in a form of a cube, 2m on an edge, parallel to the axes and centered at the origin is enclosed by a closed spherical surface with radius 3m centered at the origin. Determine the net flux crossing the closed surface given the volume charge density below Pv = x² + y c/m³arrow_forwardUsing the method of integration, what is the electric field of a uniformly charged thin circular plate (with radius R and total charge Q) at x0 distance from its center? (Consider that the surface of the plate lies in the yz plane) Use the template in the attached pictures to solve the problem.arrow_forwardConsider the surface charge distributed along the disc with an inner radius of 1m and an outer radius of 2m and a charge density of 3.uc/m2 in the figure. Since the medium is empty space, (a) Find the total charge on the disk. (b) If a 2 uC load is placed at point P1 10 cm above the axis of the load, find the force that will act on this load.arrow_forward
- The structure in the figure has 4 concentric spherical media,which have;0<r<a free spacea<r<b ρv (C/m3) constant volume charge densityb<r<c εr relative permittivityc<r free spaceFind ?⃗ , ?⃗ and ?⃗ in these 4 regions and also plot themarrow_forwardGiven a 60-uC point charge located at the origin, find the total electric flux passing through: (a) that portion of the spherer= 26 cm bounded by 0 < 0 < and = 0 <0< (b) the closed surface defined by p = 26 cm and := ±26 cm; (c) the plane := 26 cm.arrow_forwardCoaxial conducting cylinders are located at ? = 0.5 cm and ? = 1.2 cm. The region betweenthe cylinders is filled with a homogeneous perfect dielectric. If the inner cylinder is at 100 V and the outer is at 0V, find(a) the location of the 10 V equipotential surface;(b) the maximum value of electric field ( ????? );(c) the dielectric constant of the medium (??), if the charge per meter length on theinner cylinder is 10 nC/m.arrow_forward
- A 20-nC point charge is at the origin in free space. Calculate V1 if pointP1 is located at P1(2, 3,−1) and V = 0 at (6, 5, 4).arrow_forwardConsider two concentric spherical shells--one conducting and one non-conducting. The conducting spherical shell has radius 3 cm and total charge of -8 nC, while the non-conducting spherical shell, which is outside the conducting shell, has inner radius 8 cm, outer radius 14 cm, and total charge 5 nC. Determine how strong the electric field is, in kV/m, 10 cm from the center of the conducting shell.arrow_forwardPlease answer and write neatly. (Show your complete solution.) Volume charge density is located in free space as ρν = 2e−1000r nC/m3for 0 < r < 1 mm, and ρν = 0elsewhere.(a) Find the total charge enclosed by the spherical surface r = 1 mm.(b) By using Gauss’s law, calculate the value of Dr on the surface r = 1 mm.arrow_forward
- A solid metallic sphere of radius a carries total chargeQ. No other charges are nearby. The electric fieldjust outside its surface is keQ /a2 radially outward. Atthis close point, the uniformly charged surface of thesphere looks exactly like a uniform flat sheet of charge.Is the electric field here given by s/P0 or by s/2P0?arrow_forwardA charge located at the origin in free space produces a fields for which Ez=2kV/m at point P(-2, 4, -1). Find Q in microcoulombs.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
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