What is the Proportionality of Electrostatic Potential at a Distance?

[Reshma]

Homework Statement

(Objective type question)
Consider a square ABCD of side a, with charges +q, -q, +q, -q placed at the vertices, A, B, C, D in a clockwise manner. The electrostatic potential at some point located at distances r(r>>a) is proportional to?

Homework Equations

$$V =\frac{1}{4\pi \epsilon_0}\sum_i \frac{q_i}{R_i}$$

The Attempt at a Solution

From the equation for the electrostatic potential is the obvious that V will be proportional to 1/r. I am a little confused by the options given to me...so just want to confirm.

Other options:
a] Constant
b] 1/r^2
c] 1/r^3

 

[neelakash]

Hi reshma,it is the 1/r^3 which is the correct answer.Note that it is a quadrupole...You may wish to refer to Griffiths page 147.

 

[Reshma]

Thanks a billion, neelakash! I knew something was fishy with my answer...I never thought of the quadrapole moment.

 

[neelakash]

Reshma,I have sent you a PM regarding studies...Plesae pm back me or send email at
neelakash2007@rediffmail.com