Physics for Scientists and Engineers: Foundations and Connections
1st Edition
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Katz, Debora M.
Chapter34: Maxwell’s Equations And Electromagnetic Waves
Section: Chapter Questions
Problem 18PQ
Related questions
Question
An electric dipole is located along the y axis as shown in Figure P24.48. The magnitude of its electric dipole moment is defined as p = 2aq. (a) At a point P, which is far from the dipole (r ≫ a), show that the electric potential is
(b) Calculate the radial component Er and the perpendicular component Eθ of the associated electric field. Note that Eθ = −(1/r)(∂V/∂θ). Do these results seem reasonable for (c) θ = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement shown in Figure P24.48, express V in terms of Cartesian coordinates using r = (x
2 + y
2
)
1/2 and
(f) Using these results and again taking r ≫ a, calculate the field components Ex and
Ey
.
![Figure P24.48](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F90ca5e3f-35a0-404b-9063-b2aaed153907%2F209191a5-5b2b-40c4-9273-9f4915c03800%2Fv9ztyy_processed.png&w=3840&q=75)
Transcribed Image Text:Figure P24.48
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