Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 2, Problem 2.23P
A disk of radius a in the xy plane carries surface charge of density P1=pr0/pC/m2 where pω is a constant. Find the electric field intensity E everywhere on the z axis.
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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.
A hollow sphere, with inner radius a and outer radius b, has a volumetric charge distribution p = kr^2, where r is the distance from the center of the sphere outwards and k is a known constant. Using Gauss's law, find the electric field at r < a, a < r < b, and r > b, and graph the electric field as a function of r.
can you please solve this question, thanks.
A sheet of charge, m , is present at the plane x = 3 in free space, and a line charge of
rL = 20 nC/m , is located at x = 1, z = 4. (a) Find the magnitude of the electric field intensity at the
origin. (b) Find the direction of E at P(4,5,6)
Chapter 2 Solutions
Engineering Electromagnetics
Ch. 2 - Three point charges of equal magnitude q, that...Ch. 2 - Point charges of 1nC and -2 nC are located...Ch. 2 - Point charges of 50 nC each are located at...Ch. 2 - Eight identical point charges of Q C each are...Ch. 2 - A point charge of 3 nC is located at the point...Ch. 2 - Two point charges of equal magnitude q are...Ch. 2 - Point charges of equal magnitude but of opposite...Ch. 2 - A crude device for measuring charge consists of...Ch. 2 - A 100-nCpoint charges is located at A(-1,1,3)in...Ch. 2 - A configuration of point charges consists of a...
Ch. 2 - A charge Q0 located at the origin in free product...Ch. 2 - Electrons are in random in a fixed region in...Ch. 2 - A uniform volume charge density of 0.2 μC/m3 is...Ch. 2 - The electron beam in a certain cathode ray tube...Ch. 2 - A spherical volume having a 2-/μm radius contains...Ch. 2 - Within a region of free space, charge density...Ch. 2 - A length d of the charge lies on the Z-axis infree...Ch. 2 - (a) Find E in the plane z=0 that is produced by a...Ch. 2 - A line having charge density p0|C|C/m and of...Ch. 2 - A line charge of uniform charge density p0 C/m and...Ch. 2 - A charged filament forms a circle of radius a in...Ch. 2 - Prob. 2.22PCh. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric field on the z-axis produced...Ch. 2 - A disk of radius a in the xy plane carries surface...Ch. 2 - (a) Find the electric intensity on the z- axis...Ch. 2 - Given the electric field E=(4x2y)ax(2x+4y)ay, find...Ch. 2 - An electric dipole (introduced in Problem 2.7, and...Ch. 2 - If E=20e5y(cos5xaxsin5xay) ,find (a)...Ch. 2 - For fields that do not vary with z in cylindrical...
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- In 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_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_forwardA sheet of charge, ρS = 2nC/m2, is pressed at the plane x = 3 in free space, and a line charge, ρL = 20nC/m, is located at x = 1, z = 4. Find the magnitude of the electric field intensity at the origin. (Hint: E = ES + EL)arrow_forward
- Please 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_forwardA solid copper sphere of radius 20 cm carries a charge of 50 nC. Using Gauss' Law find the electric field (a) 16 cm, (b) 20 cm, and (c) 100 cm from the center of the sphere.arrow_forwardFind the electric field intensity at the point P due to a uniform line charge (ρL) lying along the x- axis and extending from- (4) to + (4) , Where the coordinates of the point P(3,3,4)arrow_forward
- A uniform line charge and a uniform sheet charge, both infinite in extent, are located in free space along the y-axis and at x = -1 respectively. Determine E at point M(2, -1, 1) if the line charge density is 15 nc/m and the sheet charge density is 2 nC/m^2arrow_forwardGiven the field: D = 20 [-sinØ ap + sin 2Ø aØ] Find the total charge lying within the volume 1<p < 2,0 < Ø < π, and 0 < z < 1 by evaluating both sides of the Divergence Theorem equationarrow_forwardFind |E| at the origin in free space if a uniform line charge of 30 nC/m lies along the line (y = 3, z = 5).arrow_forward
- In free space, q1 = 3nC charges are placed on y = 1 and y = 6, respectively, on the y-axis as shown in the figure. Accordingly, what is the electric potential value at y = 4?arrow_forwardA 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_forwardQ/Find the electric field intensity at the point (P) due to a uniform line charge (ρL) lying along the x- axis and extending from (-4) to (+4) , Where the coordinates of the point P(3,3,4) ??arrow_forward
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