An electric dipole consists of two charges of equal magnitude and opposite sign

Question

An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance 2a as shown in the figure below. The dipole is along the x axis and is centered at the origin. The electric potential at point R on the positive x axis is given by the following equation: VR = When x is much greater than a, the following approximation can be used: (a) Use the information above to find the electric potential created by the dipole described above at the point (3a, 0). (Use any variable or symbol stated above along with the following as necessary: ke.) (b) By what percentage does your answer differ from the result of the approximate expression that is valid when x is much greater than a.

Explanation / Answer

a)
The equation of electric potential is given as
VR = - 2ke q a / (x2 - a2)
The electric potential at the potential at (3a, 0) is,
VR = - 2ke q a / ((3a)2 - a2) = - ke q/4a.

b)
Using the approximation, the formula for potential is
VR appr = - 2ke q a / x2
The potential at the potential at (3a, 0) is,
VR appr = - 2ke q/9a.
Percentage error = [(VR - VR appr) / VR ]x 100 = 11.11%

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