Concept explainers
Point charges of equal magnitude but of opposite sign are positioned the charge +q at z = -d/2 and charge -q at z= -d/2 The charges in this configuration form an e1ectric dispole (a) Find the electric field intensity E everywhere on the z-axis is (b) Evaluate pan a result at the origin
(c) Find the electric geld intensity everywhere on the zy plane, expressing your result as a function of radius p in cylindrical coordinates, (d) Evaluate your pan c result at the origin (e) Simplify your part c result for the case in which p >> d.
(a)
The electric field intensity on z -axis.
Answer to Problem 2.7P
The required electric field intensity is:
Explanation of Solution
Given Information:
The point charge
Calculation:
Let
Conclusion:
The required electric field intensity is:
(b)
The electric field intensity at origin.
Answer to Problem 2.7P
The required electric field intensity is,
Explanation of Solution
Given Information:
The point charge
Calculation:
The electric field at origin,
Conclusion:
The required electric field intensity is
(c)
The electric field intensity on x-y plane as a function of radius in cylindrical coordinates.
Answer to Problem 2.7P
The required electric field intensity is
Explanation of Solution
Given Information:
The point charge
Calculation:
Let
Conclusion:
The required electric field intensity is
(d)
The electric field intensity at origin.
Answer to Problem 2.7P
The required electric field intensity is
Explanation of Solution
Given Information:
The point charge
Calculation:
The electric field intensity at origin,
Conclusion:
The required electric field intensity is
(e)
The electric field intensity on x-y plane when
Answer to Problem 2.7P
The required electric field intensity is,
Explanation of Solution
Given Information:
The point charge
Calculation:
When
Conclusion:
The required electric field intensity is
Want to see more full solutions like this?
Chapter 2 Solutions
Engineering Electromagnetics
- A solid conducting sphere with radius R that carries positive charge Q is concentric with a very thin insulating shell of radius 2R that also carries charge Q. The charge Q is distributed uniformly over theinsulating shell. (a) Find the electric field (magnitude and direction) in each of the regions 0 < r < R, R < r < 2R, and r > 2R. (b) Graph the electric-field magnitude as a function of r.arrow_forwardThere 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 field on charge q1. Consider that the charges q1, q2 and q3 are equal to q.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_forward
- Calculate 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_forwardCalculate the electric field intensity E at M(3, -4, 2) in free space caused by: a. Charge Q1 = 2 µC at P1(0, 0, 0) b. Charge Q2 = 3 µC at P2(-1, 2, 3) c. Charge Q3 = 4 µC at P3(-3, -2, 4) d. The total field intensity of the 3 charges ( please provide complete solutions, thank you )arrow_forwardPlease 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_forward
- 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.arrow_forwardIn empty space there is (-∞, 0) semi-infinite linear uniform and constant charge density ρl = 4 [C / m] on the z-axis. Calculate the electrostatic field that this charge density will create at point A (5,0,0). ke = 1 / 4πεWrite numerically the components of the electrostatic field in terms of the given quantities.arrow_forwardThree infinite uniform sheets of charge are located in free space as follows: -7 nC/m2 at y = 3, -4 nC/m2 at y = -4, and 9 nC/m2 at y = 0. Find magnitude of E at the point PA(9, 14,-7).arrow_forward
- Given 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_forwardTwo spherical charges with radius R = 1m and radius R = 1.5m in free space appear as. The volumetric charge densities in both spheres are the same and \ rho ρv1 = ρv2 = 3μC / m ^ 3. The distance between the two spheres from outside to outside is d = 0.5m. Find the magnitude and direction of the electric field at point P on the circle of radius R = 1m from the center of the large sphere.arrow_forwardA line charge of uniform charge density ρ0 C/m and of length L is oriented along the z axis at −L/2 < z < L/2. (a) Find the electric field strength, E, in magnitude and direction at any position along the x axis. (b) With the given line charge in position, find the force acting on an identical line charge that is oriented along the x- axis at L/2 < x < 3L/2.arrow_forward
- Introductory Circuit Analysis (13th Edition)Electrical EngineeringISBN:9780133923605Author:Robert L. BoylestadPublisher:PEARSONDelmar's Standard Textbook Of ElectricityElectrical EngineeringISBN:9781337900348Author:Stephen L. HermanPublisher:Cengage LearningProgrammable Logic ControllersElectrical EngineeringISBN:9780073373843Author:Frank D. PetruzellaPublisher:McGraw-Hill Education
- Fundamentals of Electric CircuitsElectrical EngineeringISBN:9780078028229Author:Charles K Alexander, Matthew SadikuPublisher:McGraw-Hill EducationElectric Circuits. (11th Edition)Electrical EngineeringISBN:9780134746968Author:James W. Nilsson, Susan RiedelPublisher:PEARSONEngineering ElectromagneticsElectrical EngineeringISBN:9780078028151Author:Hayt, William H. (william Hart), Jr, BUCK, John A.Publisher:Mcgraw-hill Education,