Calculate V and E, at a point on the x-axis far from the dipole. SOLUTION (For the next two answers, use the following as necesary: ke, q, a, and x.) For point R far from the dipole such that x >> a, neglect a2 in the denominator of the answer to part (b) and write V in this limit: 2kega - m.() VR = lim x >>a (x >> a) Use Ex AP and this result to calculate the x-component of the electric field at a point on the x-axis far from the dipole: dx 2kega E, - - -- (- ) dv d. dx dx x2 = 2k (x >> a) =

Calculate V and E, at a point on the x-axis far from the dipole. SOLUTION (For the next two answers, use the following as necesary: ke, q, a, and x.) For point R far from the dipole such that x >> a, neglect a2 in the denominator of the answer to part (b) and write V in this limit: 2kega - m.() VR = lim x >>a (x >> a) Use Ex AP and this result to calculate the x-component of the electric field at a point on the x-axis far from the dipole: dx 2kega E, - - -- (- ) dv d. dx dx x2 = 2k (x >> a) =

An Introduction to Physical Science

14th Edition

ISBN:9781305079137

Author:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Publisher:James Shipman, Jerry D. Wilson, Charles A. Higgins, Omar Torres

Chapter8: Electricity And Magnetism

Section: Chapter Questions

Problem 1SA

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Concept explainers

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.

Question

Calculate V and E, at a point on the x-axis far from the dipole.
SOLUTION
(For the next two answers, use the following as necesary: ke, q, a, and x.)
For point R far from the dipole such that x >> a, neglect a2 in the denominator of the answer to part (b) and write V in this limit:
2kega
VR = lim
x
>>a
(x >> a)
Use Ex
AP
and this result to calculate the x-component of the electric field at a point on the x-axis far from the dipole:
dx
2kega
E, - - -- (- )
dv
d.
dx
dx
x2
= 2k
(x >> a)
=

An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance 2a as shown in the figure. The dipole is along the x-axis and is centered at the origin.
An electric dipole located on the x-axis.
R
a

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