48. 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>> %3D a), show that the electric potential is V = kpcos0 (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(@V/80). Do these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement shown in Figure P25.71, express V in terms * Cartesian coordinates using r = (x² +y³)"² and y cos 0 = (f) Using these results and again taking r>> a, calculate the field ? + y²)/2 components Ex and E,
48. 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>> %3D a), show that the electric potential is V = kpcos0 (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(@V/80). Do these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement shown in Figure P25.71, express V in terms * Cartesian coordinates using r = (x² +y³)"² and y cos 0 = (f) Using these results and again taking r>> a, calculate the field ? + y²)/2 components Ex and E,
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Need help for questions (d), (e), and (f).
![E,
P
Ee
+q+
a
Figure P24.48](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c93ea27-b40b-4f72-864c-e189cb0db2fa%2F47c5543f-c84a-42cf-b81e-b88e7e87ef45%2Fu70fdt9_processed.png&w=3840&q=75)
Transcribed Image Text:E,
P
Ee
+q+
a
Figure P24.48
![48. 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>>
%3D
a), show that the electric potential is V =
k.pcos0
(b) Calculate the radial component E, and
the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(@V/ô0). Do
these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement
shown in Figure P25.71, express V in terms of Cartesian coordinates using r = (x² +y³)'"2 and
y
cos 0 =
(x² + y²)"²
(f) Using these results and again taking r >> a, calculate the field
1/2
components Ex and E,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4c93ea27-b40b-4f72-864c-e189cb0db2fa%2F47c5543f-c84a-42cf-b81e-b88e7e87ef45%2F6lj46k8_processed.png&w=3840&q=75)
Transcribed Image Text:48. 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>>
%3D
a), show that the electric potential is V =
k.pcos0
(b) Calculate the radial component E, and
the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(@V/ô0). Do
these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement
shown in Figure P25.71, express V in terms of Cartesian coordinates using r = (x² +y³)'"2 and
y
cos 0 =
(x² + y²)"²
(f) Using these results and again taking r >> a, calculate the field
1/2
components Ex and E,
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