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Chapter 2 Solutions
Fundamentals of Electromagnetics with Engineering Applications
- There is an arrangement of three charges distributed along a perimeter of a circumference, the charge q1, is located at the point r1 = r with an angle of 900, q2, is located at the point r2 = r with an angle of 1500, q3, is located at the point r3 = r with an angle of 300. Calculate the electric potential on charge q1. Consider that the charges q1, q2 and q3 are equal to q.arrow_forwardA cylinder with a base radius R and a height of 2L is charged over a surface with a constant surface density o (see Figure 1.12). Assuming that the bases of the cylinder do not carry a charge, determine the strength of the electrostatic field at point M on the axis of the cylinder at a distance a from its center.arrow_forwardElectrical Engineering 1. The point charges of +Q at (-1,0), +Q at (1,0), and -2Q at (0,1) lie in a plane where z = 0, respectively. At this time, find the electric flux density at (0,0).arrow_forward
- 4) Find the option that correctly expresses the total force and Electric Field acting on a 1m-radius ring with a charge density of ρi = 5 nC / m at the center of the xy plane, due to the body with an infinitely large shallow charge density ρs = 5ε0 nC / m2 located in the plane z = 10m. A) E=2.5 ay ; F=5π10-9arN B) E=2.5 ay ; F=25π10-9ayN C) E=2.5 az ; F=25π10-9azN D) None. E) 0 this is an electromagnetic wave lesson question.arrow_forwardTwo point charges 5 nC and -2 nC are located at (2, 0, -4) and (-3, 0, 5) respectively,a. Find the force on a 10 nC point charge located at (-1, -3, 7),b. Calculate the electric field at (-1, -3, 7).arrow_forwardInside a sphere of radius a is a volumetric charge distribution with a density expressed in spherical coordinates as pv = k0 / r2 [C / m3]. Show that the equation div(D) = pv is satisfied by calculating div(D) inside and outside the sphere.arrow_forward
- Three uniform charge distributions are present in a region: an infinite line charge, an infinite sheet of charge, and a finite line charge. An infinite line charge has a charge density pL = -2 nC/m is located at (x, 0, 4); an infinite sheet of charge located at (x, y,-7) with a charge density pS = -3 nC/m 2 ;a finite line charge that spans from (0, -3, 0) to (0, 3, 0) with a charge density of pL = 4 nC/m. Indicate the formulas that you will use. All coordinates are in meters. Use k=9 x 10 9. Determine the electric field due to the infinite line charge at (0, 0, 3). Determine the electric field due to the infinite sheet charge at (0, 0, 3). Determine the electric field due to the finite line charge at (0, 0, 3). Determine the total electric field at (0, 0, 3) due to the three charge distributions.arrow_forwardTwo bidirectionally infinite line charges exist in vacuum. One has a charge density of -9 nC/m at x = -3, y = -9, while the other has a charge density of 7 nC/m at y = -6, z = -5. Determine the y-component of the electric field in V/m at (3, 4, 4). All coordinates are measured in meters.arrow_forwardA sphere has radius of R. The sphere also has a uniform charge of 4Q. There is a point charge of -Q at sphere's center. Derive an equation for E at points where the radius is less then R.arrow_forward
- A uniform sheet of charge with ρs = ―1/3? nC/m2 is located at z = 5 m and a uniform line of charge with ρL = ―25/9 nC/m is located at z = -3 m and y = 3 m. Find E at (0,-1,0).arrow_forwardLet D = 6xy3z2 ax + 7xyz4 ay + 8x5y4 az PC/m2 in free space, Answer all questions (a)Find the total electric flux passing through the surface y = 4, 0 ≤ x ≤ 3, 0 ≤ z ≤ 2 in a direction away from the origin. (b) Find the force |F| on the charge Q1(30 mC) at P(4,1,6)? (c) Find the total charge contained in an incremental sphere having a diameter of 8 mm centered at P (4, 1, 6)?arrow_forwardCalculate D in rectangular coordinates at point P(2,-3,6) produce by: (a) a point charge QA=55 mC at Q(-2,3,-6); (b) a uniform line charge ρLB=20mCmρLB=20mCm on the x axis; (c) a uniform surface charge density ρSC=120μCm2ρSC=120μCm2on the plane z=-5m.arrow_forward
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