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 >> a), show that the electric potential is V=KePCos0 (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(ðV/20). Do these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement
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 >> a), show that the electric potential is V=KePCos0 (b) Calculate the radial component E, and the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(ðV/20). Do these results seem reasonable for (c) 0 = 90° and 0°? (d) For r = 0? (e) For the dipole arrangement
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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 >>
a), show that the electric potential is V =-
KePcos0
(b) Calculate the radial component E, and
the perpendicular component E, of the associated electric field. Note that E, =-(1/r)(@V/20). 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
cos e =
o (f) Using these results and again taking r >> a, calculate the field
(x² + y?)2
components E, and E,
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