Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 2, Problem 2.15P
A spherical volume having a 2-/μm radius contains a uniform volume charge density of 105 C/m3. (a) what total charge is enclosed in the spherical volume? (b) Now assume that a large region contains one of these title spheres at every corner of a cubical grid 3 mm on a side and that there is no charge between the sphere. What is the average volume charge density through out this large region?
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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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- Example An insulating solid sphere of radius a has a uniform volume charge density ρ and carries a total positive charge Q. (A) Calculate the magnitude of the electric field at a point outside the sphere. (B) Find the magnitude of the electric field at a point inside the spherarrow_forwardA spherical shell of inner and outer radii 4.39 meters and 12.80 meters, respectively, has a total charge of 14.55 nanocoulombs. Find the magnitude of the electric field, in volts per meter, 9.12 meters from the center of the shell.arrow_forwardA solid sphere of radius R has a nonuniform charge distribution ρ = Ar^2 , where A is a constant. Determine the total charge, Q, within the volume of the sphere. show solutionarrow_forward
- A solid sphere of diameter 20 cm has a non-uniform charge density where A = 0.600 x 10-14 C/m5. Determine the total charge, Q, within the volume of the sphere.arrow_forwardTwo bidirectionally infinite line charges exist in vacuum. One has a charge density of -7 nC/m at x = -3, y = -4, while the other has a charge density of 7 nC/m at y = -1, z = -2. Determine the y-component of the electric field in V/m at (8, 1, 2). All coordinates are measured in meters.arrow_forwardA sphere carries a uniform volume charge density of 6.39 nC/m3. If the sphere's radius increases be a factor of 2 and the charge in it increases by a factor of 3, find the new volume charge density of the sphere in nC/m3. Do not scientific notation.arrow_forward
- Determine the total charge present throughout the shell if a uniform volume charge density of 18 μC/m^3 is present throughout the spherical shell extending from r=3 cm to r=5 cmarrow_forwardQ (1): Infinite uniform line charges of 2 nC / m lie along the x and y axes in free space. Find E and D at PA (1, 2, 3).arrow_forwardPlease explain what locus is and how to solve. A 100-nC point charge is located at A(−1, 1, 3) in free space. (a) Find the locus of all points P(x, y, z) at which Ex = 500 V/m. (b) Find y1 if P(0, y1, 3) lies on that locus.arrow_forward
- A uniform sheet charge, infinite in extent, is located at x=2 m. Given that the charge density is 5 nC/m^2, determine E at the origin.arrow_forwardWithin the sphere defined by r ≤ 8 cm, the volume charge density is ρv = 6.8 x 10-7 C/m3 . (i) Find an expression for electric field intensity for region r < 8 cm. Hence, calculate the electric field intensity at a point having rectangular coordinates of (x, y, z) = ( 3 cm, 2cm, 0 ). (ii) Assume that all of the electric charge is removed from a spherical region centered at (x, y, z) =(3 cm, 0, 0) and having a radius of 1 cm. Calculate the total electric field intensity at point (x,y,z) = (3 cm, 2 cm, 0).arrow_forwardA square plate residing in the x-y plane is situated in the space defined by -3 m ≤x≤3 m and -3 msys3 m. Find the total charge on the plate if the surface charge density is P₁ = 4y² (uC/m²).arrow_forward
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