Coulomb's Law: Attraction/Repulsion & Approximate Force Calculation

[kyrax]

Homework Statement

Consider the two parallel electric dipoles shown.


+ (Q) + (Q) | (Distance=d/2)
------------------------------------------x------
- (-Q) - (-Q) | (Distance=d/2)
|-------Distance=X-----------|

a) Do the two dipoles attract or repel from each other
b) Let x>>d. Find an approximate expression for the force between the two dipoles. The expression is in terms of Q,d, and x.
C) sketch the graph of F vs. x.

Homework Equations

Coulombs's law
F=k(q₁q₂/r²

The Attempt at a Solution

I an completely new to Coulomb's law and dipoles so i don't know how to start.

a) The answer is they repel but i don't get why. I know the top/bottom two charges will repel but won't they attract each other diagonally?
b)Have not attempted. Don't know how to start.
c) Stuck on b. didnt get to this yet

 

[diazona]

I'm guessing your diagram was supposed to look like this?

   + (Q)                        + (Q)
   |                            |      (Distance=d/2)
 --x----------------------------x-----------
   |                            |      (Distance=d/2)
   - (-Q)                       - (-Q)
   |-------Distance=x-----------|

Forget about the fact that they're dipoles. Just think about it as a set of four charges at the corners of a rectangle, and figure out the force on each charge. You don't need the exact magnitude and direction (at least not for part a), but you can easily figure out whether there's more force acting to the left or the right on any particular charge.

 

[kyrax]

I'm guessing your diagram was supposed to look like this?

   + (Q)                        + (Q)
   |                            |      (Distance=d/2)
 --x----------------------------x-----------
   |                            |      (Distance=d/2)
   - (-Q)                       - (-Q)
   |-------Distance=x-----------|

Forget about the fact that they're dipoles. Just think about it as a set of four charges at the corners of a rectangle, and figure out the force on each charge. You don't need the exact magnitude and direction (at least not for part a), but you can easily figure out whether there's more force acting to the left or the right on any particular charge.

yes, it should look like that. thanks.

i don't know how to find the forces.
would it be like this? assuming the Q's are: Q₁(top left), Q₂(top right), -Q₃(bottom left), -Q₄(bottom right)

F_Q1=[k(Q₁Q₂)/x²]+[k(Q₁-Q₃)/d²]+[k(Q₁-Q₄)/(x²+^d2)]?

and i do this for Q₂, -Q₃, -Q₄?

 

[ideasrule]

No equations needed for part a. Just think: the charge at the upper-left is repelled by one of the charges on the right and attracted by another. Which force is greater? Ditto for the charge at the lower-left.