Electric Field and infinite line of charge

[soccerref14]

Can someone show me or give me an idea on how to start this problem.

Show that an infinite line of charge with linear charge density lamda exerts an attractive force on an electric dipole with magnitude F = (2)(Lamda)(p) / (4)(pie)(Epsilon knot)(r^2). Assume that r is much larger than the charge separation in the dipole.

 

[praharmitra]

You can assume the linear charge density to be along the x-axis, and keep your origin such that the point at which force is to be calculated lies on the y-axis at a distance of $$r$$.

start with taking a small element $$dx$$ at a distance x.

Since linear charge density is $$\lambda$$, the charge on that element is $$\lambda(dx)$$

Find the force on the dipole by this element and then integrate over the entire length of the charge. Don't forget that force is a vector, and integration should be done along the respective components.