Dipole in polar coordinates

DaraRychenkova
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?

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Answers and Replies

Science Advisor
Homework Helper
Gold Member
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?

MatinSAR, vanhees71 and PhDeezNutz
Science Advisor
Gold Member
2022 Award
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!

MatinSAR