Optimizing Polar Axis for Dipole in Polar Coordinates

In summary, the conversation discusses finding the potential and electric field in a previous problem, with the formula for the potential being provided. The speaker also asks for clarification on the relationship between the potential and field, and provides a coordinate-free notation for the electric field. The conversation ends with a suggestion to choose the polar axis wisely in order to solve the problem quickly.
  • #1
DaraRychenkova
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Homework Statement
- Determination of the dipole (p=ql). Find the dipole potential at a distance r much larger than the size of the dipole itself. Calculate the field of the dipole using the relationship between the potential and the field.



1. Solve the problem of finding the dipole field using the expression for the potential obtained in the previous problem in polar coordinates
Relevant Equations
Dipole, electrostatic
I don't know how to get the result referring to the previous task. Is my decision correct?
IMG_20230317_145638.jpg
 

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  • #2
The potential in the "previous problem" is probably something like $$V=\frac{1}{4\pi\epsilon_0}\frac{\mathbf{p}\cdot\mathbf{r}}{r^3}.$$ If it is in some other form, use that. What do you think "the relationship between the potential and the field" is?
 
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  • #3
I can't make sense of the posted scan. Obviously you've given the electric field in coordinate-free notation,
$$\vec{E}=\frac{1}{4 \pi \epsilon_0 r^5}(3 \vec{r} \vec{r} \cdot \vec{p}-r^2 \vec{p}).$$
Now first think about, how to choose your polar axis. With the right choice, it's very quickly solved!
 
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