What is the electric field strength of a dipole rod on the x axis?

[the7piano]

Homework Statement

A rod of length 2L lies on the x axis, centered at the origen, and carries a line charge

density given by t=T(x/L), where T is a constant. (a) Find an expression for the electric

field strength at points on the x axis, for x>L (b) Show that for x>>L, your result has the

1/x^3 dependence of a dipole field, and by comparison, determine the dipole moment of the

rod.

Homework Equations

dE = (k dq)/r^2

The Attempt at a Solution

dq=Tda, dE= (k dq)/(x-a)^2 = (kT/L) * (a da) / (x-a)^2

integral dE form -L to +L

E = (kT/L) * ( - x/(x+L) + x/(x-L) + ln( (x-L)/(x+L)) )

when x>>L , by using binomial expanding, the result what I have

1/x^2 dependence. Help !

 

[mezarashi]

Could I get confirmation on this question? Normally when electric dipoles are talked of, we would look to find fields for distances perpendicular to the dipole rather than parallel.

 

[the7piano]

The situation fof that problem, To find the fields for distances parallel to the dipole.

I think it doesn't matter whether perpendicular or parallel.

The result of both situation has 1/^3 dependence of a dipole field, I think

If you know the answer about perpendicular case, I really appreciate your sincerity

although that is not exact answer about this problem. Thank you for your reply.