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 V=: k pcose (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(ôV/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 +y)"2 and 1/2 y cos 0 : (x² +y²)"2 (f) Using these results and again taking r >> a, calculate the field components E and E,

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 V=: k pcose (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(ôV/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 +y)"2 and 1/2 y cos 0 : (x² +y²)"2 (f) Using these results and again taking r >> a, calculate the field components E and E,

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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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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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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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