Electric Force Between Water and Chlorine

[dchrisma]

Homework Statement

The dipole moment of the water molecule is 6.17 x 10^-31 C*m . Consider a water molecule located at the origin whose dipole moment points in the +x-direction. A chlorine ion , of charge -1.60*10^-19, is located at x= 3.00*10^-3 m.

Assume that x is much larger than the separation d between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis can be used.

Question: Find the magnitude of the electric force that the water molecule exerts on the chlorine ion.

Homework Equations

p=qd

F= k(q1q2)/d^2

The Attempt at a Solution

Not sure what to do at this point. I tried to use the electric dipole moment equation to find the charge of the water molecule since p and d
were given. Knowing that charge, I placed the variables into the force equation but to no avail. There's definitely more to this than I'm seeing. Isn't that force equation only related to point charges? I don't believe either particle is a point charge in this case. Can someone send me in the right direction?

 

[Mindscrape]

What kind of dipole equations do you have? I'll give you a couple equations I know

$$V_{dip} = k \frac{\mathbf{p} \cdot \mathbf{\hat{r}}}{r^2}$$

$$\matbf{p} = q \mathbf{d}$$

Your method sounds correct if your equations and work are correct, perhaps you could post those also? Find the electric field of the dipole, and then use the fact that F=qE.

 

[nucleusfermi]

First find E vector through [kp{1+3cos^2x}^1\2]/r^3 (r=distance from middle point of dipole to the treated charge i.e. Cl ion.) For your case it will reduced as [2kp/r^3] and then use Electric Force= Charge * Electric Field, hope this will derive the proper answer. [For P (Charge*Distance).] In this operation we believe Cl charge is pretty minor.

This case can be made more interesting if we consider another dipole instead of Cl ion, in that case Electric Force will be proportional to (Distance)^-4 I think.

I got a strange idea as well, can we take "Reduced Charge" like we do for mass, means geometric mean of that? I know it's a bit hilarious as we are quite sure about quantization of charge and not the case with mass :)

I think I won't be able to track it back as very less active over internet, if someone has something obliging then can suggest @ nucleusfermi@yahoo.co.in