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University Physics Volume 2
18th Edition
ISBN:9781938168161
Author:OpenStax
Publisher:OpenStax
Chapter6: Gauss's Law
Section: Chapter Questions
Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...
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Question 3. The Electric field of a Dipole far from the
Dipole in Spherical Coordinates
LEGO
In class we found V far from the dipole in spherical coordinates. Here you will use the gradient in
spherical coordinates to obtain the E field from this potential. The results are easier to analyse than the
expressions obtained in class in Cartesian coordinates.
The dipole is along the z-axis and the point P is over the x-axis, where the azimuthal angle o = 0°. This
is why our potential is only a function of r and 0:
(p cose
V = ke
E is the negative gradient of V: E = -V. In spherical coordinates,
av
1 dv
1
av
Er
Ee=
E4=
r sin 0 ðø
ar
r d0
Transcribed Image Text:Question 3. The Electric field of a Dipole far from the Dipole in Spherical Coordinates LEGO In class we found V far from the dipole in spherical coordinates. Here you will use the gradient in spherical coordinates to obtain the E field from this potential. The results are easier to analyse than the expressions obtained in class in Cartesian coordinates. The dipole is along the z-axis and the point P is over the x-axis, where the azimuthal angle o = 0°. This is why our potential is only a function of r and 0: (p cose V = ke E is the negative gradient of V: E = -V. In spherical coordinates, av 1 dv 1 av Er Ee= E4= r sin 0 ðø ar r d0
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