How Does Dipole Interaction Energy Vary with Orientation?

In summary, the conversation discusses drawing graphs to show the dependence of interaction energy on the relative orientation of two electric dipoles. The first part has been completed and the correct expression for the interaction energy is given. However, it is unclear what the graph would look like for the case where the dipole is perpendicular to the distance vector. The conversation also mentions using LaTeX to make the equation easier to read. It is unknown what was found for the second part.
  • #1
physconomic
15
1
Homework Statement
We consider two dipoles p1 and p2 and take r to be the position vector of p2
measured from p1.

Find Uint (interaction energy)

Draw graphs showing how Uint depends upon the relative orientation of the dipoles
in the following cases:
(i) p1 is parallel to r,
(ii) p1 is perpendicular to r.
Relevant Equations
U = -p.E
UInt = 1/(4*pi*epsilon0*r^3)*[p1.p2-3(p1.r^)(p2.r^)]
Draw graphs showing how interaction energy depends upon the relative orientation of two dipoles
if
(i) p1 is parallel to r,
(ii) p1 is perpendicular to r.

I've done the first part and found the interaction energy as
UInt = 1/(4*pi*epsilon0*r^3)*[p1.p2-3(p1.r^)(p2.r^)]
which I know is correct.

I know for the perpendicular case the dot product of p1 and r would be 0 - but I'm not sure what the graph would look like.
 
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  • #2
Hello @physconomic , :welcome: !

Apparently your dipoles are electric dipoles :wink: ?

physconomic said:
which I know is correct
How so ?

For the first part, I would expect to see a graph for ##U(\theta)##, or at least the expression; I see no ##\theta ## ?

UInt = 1/(4*pi*epsilon0*r^3)*[p1.p2-3(p1.r^)(p2.r^)]
is hard to read. Perhaps you want to learn some ##\LaTeX## ?

$$U_\text{int}= {1\over 4\pi\varepsilon_0 r_{ij}^3}\Biggl[ \vec p_i\cdot\vec p_j - 3{(\vec p_i\cdot\vec r_{ij})(\vec r_{ij}\cdot\vec p_j) \over r_{ij}^2}\Biggr ]$$ is a lot easier on the eyes.

For the second part:
Well, what did you find for ##U ## ?
 
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  • #3
@physconomic wasn't seen since Wednesday .. 🤔 ?
 

Related to How Does Dipole Interaction Energy Vary with Orientation?

1. What is a dipole?

A dipole is a molecule or atom that has a separation of positive and negative charges due to differences in electronegativity between its atoms. This creates a polar molecule with a dipole moment, which is a measure of the separation of charges.

2. How do two dipoles interact?

Two dipoles can interact through electrostatic forces, where the positive end of one dipole is attracted to the negative end of another dipole. This can result in either an attractive or repulsive force between the dipoles.

3. What factors affect the strength of dipole-dipole interactions?

The strength of dipole-dipole interactions is affected by the magnitude of the dipole moments of the molecules involved, the distance between the dipoles, and the orientation of the dipoles relative to each other.

4. How do dipole-dipole interactions contribute to the properties of substances?

Dipole-dipole interactions can contribute to the overall polarity and intermolecular forces of a substance, which can affect its boiling point, melting point, and solubility in different solvents. They can also play a role in the formation of certain types of bonds, such as hydrogen bonds.

5. Can dipole-dipole interactions occur between nonpolar molecules?

No, dipole-dipole interactions can only occur between polar molecules with permanent dipole moments. Nonpolar molecules do not have a separation of charges and therefore do not experience dipole-dipole interactions.

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