COULOMB'S LAW AND ELECTRIC FIELD INTENSITY 493. A regular tetrahedron has vertices at P₁(2,0,0), P₂(-1,√3,0), P3(-1,-√3,0), andP4(0,0,2 √2). Charges of 1 mC are located at each of the four vertices. If the configura-tion is located. in free space: (a) find the magnitude of the force on each charge, and(b) the angle between any two edges of the tetrahedron.4. A point charge, Q₁ = 10 µC, is located at P₁(1,2,3) in free space, while Q₂ = -5 μC isat P₂(1,2,10). (a) Find the vector force exerted on 2₂ by 2₁. (b) Find the coordinates ofP3 at which a point charge Q3 experiences no force.5. In free space, let Q₁=10 nC be at P₁(0,-4,0), and Q₂ = 20 nC be at P₂(0,0,4). (a) FindE at the origin. (b) Where should a 30-nC point charge be located so that E = 0 at theorigin?6. A 5-nC point charge is located at A(2,-1,-3) in free space. (a) Find E at the origin.(b) Plot E(x,0,0)| vs. x, -1^x≤ 10 m. (c) What is E(x,0,0)|max?=7. A point charge, Q₁ = 1 µC; is at A(0,0,1), and QBand E, at P(1,2,3).-1 μC is at B(0,0,-1). Find E., E.,8. A 20-nC point charge is located at P(2,4,-3) in free space. (a) Find E(r). (b) Find E atA(-3,2,0). (c) Find the locus of all points at which E, = 1 V/m.9. Eight 25-nC point charges in free space are located symmetrically on a circle of radius0.2 m centered at the origin in the z = 0 plane. (a) At what point on the z axis is El amaximum? (b) What is Emax?10. Identical 1-μC point charges are located in free space at (0,0,1) and (0,0,-1). Prepare aplot showing |E| vs. z along the line x = 0, y = 2, for |z| ≤ 4.11. Eight point charges of 1 nC each are located at the corners of a cube in free space thatis 1 m on a side. Find |E| at the center of: (a) the cube; (b) a face; (c) an edge.12. A point charge Q₁, located at the origin in free space, produces a field E=r=10a, V/m for1 m. (a) Find Q₁. (b) Using this value of Q₁, find E at P(2,-1,5) in cartesian compo-nents. (c) Using the same value of Q₁, find E at C(2,2,2) in cylindrical components.13. For x, y, and z positive, let p, = 40xyz C/m³. Find the total charge within the regiondefined by: (a) 0 ≤ x,y,z ≤ 2; (b) x = 0, y = 0, 0≤ 2x + 3y ≤ 10, 0≤ z ≤ 2.14. Volume charge density within the operating region of a parallel-plate vacuum diode isgiven by p= -()eo Vod-4/3x-2/3, where the cathode is located at x = 0 and theanode at x = d. The voltage between anode and cathode is Vo. If the total charge in a1-m² cross section is -20 nC and: (a) d = 8 mm, find Vo; (b) Vo = 24 V, find d. (c) Ifd = 8 mm and Vo = 24 V, sketch p, vs. x.15. Volume charge density is given by p. = 10e-1000pe-100% C/m³. (a) Find the maximumvalue of p, in the region 0 ≤ p ≤ 0.01 m, 0 ≤ ¢ < 2π, 0 ≤ z ≤ 0.01 m. (b) Find the totalcharge contained in the first octant, where x, y, and z are positive. (c) Find b if the totalcharge found in the volume 0 ≤ p ≤ b, 0≤ ≤ π/2, z ≥ 0, is half the value found in part(b) above.and Pv0 out-16. Let p,= (x + 2y + 3z) C/m³ in the cubical region 0≤ x,y,z ≤ 1 mm,side the cube. (a) What the total charge contained within the cube? (b) Set up thevolume integral that will give E(x,0,0) for x> 1 mm. Do not integrate.=

We are authorized to answer one question at a time, since you have not mentioned which question you…

3. A regular_ tetrahedron has vertices at P₁(2,0,0), P₂(-1,√3,0), P3(-1,-√√3,0), and P4(0,0,2√2). Charges of 1 mC are located at each of the four vertices. If the configura- tion is located. in free space: (a) find the magnitude of the force on each charge, and (b) the angle between any two edges of the tetrahedron.

3. A regular_ tetrahedron has vertices at P₁(2,0,0), P₂(-1,√3,0), P3(-1,-√√3,0), and P4(0,0,2√2). Charges of 1 mC are located at each of the four vertices. If the configura- tion is located. in free space: (a) find the magnitude of the force on each charge, and (b) the angle between any two edges of the tetrahedron.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Concept explainers

Rectangular Coordinate System

In a rectangular coordinate system, each point based on the pair of coordinates is specified uniquely in the plane. From two fixed perpendicular lines, these coordinates are at a distance in the rectangular coordinate system. Each line is known as the reference axis and axes as plural. The point where they meet is called the origin (0,0).

Question

COULOMB'S LAW AND ELECTRIC FIELD INTENSITY 49
3. A regular tetrahedron has vertices at P₁(2,0,0), P₂(-1,√3,0), P3(-1,-√3,0), and
P4(0,0,2 √2). Charges of 1 mC are located at each of the four vertices. If the configura-
tion is located. in free space: (a) find the magnitude of the force on each charge, and
(b) the angle between any two edges of the tetrahedron.
4. A point charge, Q₁ = 10 µC, is located at P₁(1,2,3) in free space, while Q₂ = -5 μC is
at P₂(1,2,10). (a) Find the vector force exerted on 2₂ by 2₁. (b) Find the coordinates of
P3 at which a point charge Q3 experiences no force.
5. In free space, let Q₁
=
10 nC be at P₁(0,-4,0), and Q₂ = 20 nC be at P₂(0,0,4). (a) Find
E at the origin. (b) Where should a 30-nC point charge be located so that E = 0 at the
origin?
6. A 5-nC point charge is located at A(2,-1,-3) in free space. (a) Find E at the origin.
(b) Plot E(x,0,0)| vs. x, -1^x≤ 10 m. (c) What is E(x,0,0)|max?
=
7. A point charge, Q₁ = 1 µC; is at A(0,0,1), and QB
and E, at P(1,2,3).
-1 μC is at B(0,0,-1). Find E., E.,
8. A 20-nC point charge is located at P(2,4,-3) in free space. (a) Find E(r). (b) Find E at
A(-3,2,0). (c) Find the locus of all points at which E, = 1 V/m.
9. Eight 25-nC point charges in free space are located symmetrically on a circle of radius
0.2 m centered at the origin in the z = 0 plane. (a) At what point on the z axis is El a
maximum? (b) What is Emax?
10. Identical 1-μC point charges are located in free space at (0,0,1) and (0,0,-1). Prepare a
plot showing |E| vs. z along the line x = 0, y = 2, for |z| ≤ 4.
11. Eight point charges of 1 nC each are located at the corners of a cube in free space that
is 1 m on a side. Find |E| at the center of: (a) the cube; (b) a face; (c) an edge.
12. A point charge Q₁, located at the origin in free space, produces a field E
=
r=
10a, V/m for
1 m. (a) Find Q₁. (b) Using this value of Q₁, find E at P(2,-1,5) in cartesian compo-
nents. (c) Using the same value of Q₁, find E at C(2,2,2) in cylindrical components.
13. For x, y, and z positive, let p, = 40xyz C/m³. Find the total charge within the region
defined by: (a) 0 ≤ x,y,z ≤ 2; (b) x = 0, y = 0, 0≤ 2x + 3y ≤ 10, 0≤ z ≤ 2.
14. Volume charge density within the operating region of a parallel-plate vacuum diode is
given by p= -()eo Vod-4/3x-2/3, where the cathode is located at x = 0 and the
anode at x = d. The voltage between anode and cathode is Vo. If the total charge in a
1-m² cross section is -20 nC and: (a) d = 8 mm, find Vo; (b) Vo = 24 V, find d. (c) If
d = 8 mm and Vo = 24 V, sketch p, vs. x.
15. Volume charge density is given by p. = 10e-1000pe-100% C/m³. (a) Find the maximum
value of p, in the region 0 ≤ p ≤ 0.01 m, 0 ≤ ¢ < 2π, 0 ≤ z ≤ 0.01 m. (b) Find the total
charge contained in the first octant, where x, y, and z are positive. (c) Find b if the total
charge found in the volume 0 ≤ p ≤ b, 0≤ ≤ π/2, z ≥ 0, is half the value found in part
(b) above.
and Pv
0 out-
16. Let p,= (x + 2y + 3z) C/m³ in the cubical region 0≤ x,y,z ≤ 1 mm,
side the cube. (a) What the total charge contained within the cube? (b) Set up the
volume integral that will give E(x,0,0) for x> 1 mm. Do not integrate.
=

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