Engineering Electromagnetics
9th Edition
ISBN: 9781260029963
Author: Hayt
Publisher: MCG
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Chapter 4, Problem 4.31P
A potential field in free space is expressed as V=20 (xyz)V. (a) find the total energy stored within the cube 1
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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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- Given the potential field in cylindrical coordinates, V = 100 + 50ρ + 150ρ sinΦ volts, and point P at ρ = 1 m, Φ = 600, z = 0.5 m, find the electric field intensity E at P.arrow_forwardThere is an infinitely long cylinder of radius 0.5 cm along the z-axis, and it is filled uniformly with a volume charge density of 3.5 C/m3. Apply Gauss’s Law to find an expression for the electric field in two cases: a) For ρ > 0.5cm b) For 0 <ρ<0.5 cmarrow_forwardIn free space, q1 = 4nC 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_forward
- Three point and positive electric charges are located at the vertices of an equilateral triangle with side √3m. Two of them have charge q and the third has charge 2q, where q = 10−4C. Calculate the electric field at the midpoint of the side on which the smallest charges lie (point P).arrow_forwardIn a certain region of space, the electrical potential is given by the relationship V (x, y, z) = Axy- Bx² + Cy where A, B and C are constant. Calculate as x, y and z components of the electric field. (b) in which points (x, y, z) is the electric field equal to zero?arrow_forwardExample 2.24) In the two-layer uniformly varying field electrode system separated by the X=0 plane, the amplitude of the electric field vector in the first layer is 80kV/cm and the angle it makes with the perpendicular component is 〖20〗^0. Since the relative electric constants of the layers are 4 and 2, respectively, calculate the tangential component of the electric field in the second layer.arrow_forward
- The expression of a potential field is given as follows: V=2x²+4y³z Determine the magnitude of the electric field instensity vector E at the point (2,4,3) and the unit vector in the direction of the electric field instensity at the same point.arrow_forwardCompute for the potential at A(5, 0, -1) if the potential at the origin is -5 MV in a region in vacuum where the electric field is produced by a 15-mC point charge on (-2, 4, 3). All coordinates are measured in meters. a.) -15.0689 MV b.) -20.6705 MV c.) -10.0689 MV d.) -5.6705 MVarrow_forwardA point charge of 30 nC is located at the origin while plane y = 3 carries charge 10nC/m2. Find D at (0,4, 3).arrow_forward
- Determine the volume charge density, in pC/m3, at (9, -3, 8) if the electric field present in the region is E = sin (3 x + 2 y + 2 z)(ax + ay + az) V/m. All coordinates are measured in meters.arrow_forwardElectromagnetics. A spherical surface has following range. Find volume of spherical surface.arrow_forwardA sheet of charge , ρs = 2nC/m2 is present at the plane x =3 infree space, and a line charge , ρL = 20nC is located at x=1, z=4.Find the magnitude of the E at the origin. Complete solution.arrow_forward
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