# Dipole above infnite conductor

• I
In summary: I'm not seeing a reason to delete this.In summary, the conversation discusses an electric dipole p with an arbitrary direction and distance a from a plane infinite conductor at z=0. The dipole is represented by two equations, p=(2pcos\theta \hat{z}+psin\theta \hat{x}) and p'=(2p'cos\theta \hat{z}-p'sin\theta \hat{x}), and the resulting charge distribution is calculated using Maxwell's laws. There is some confusion about a 2 in the equations, but the conversation ends with the issue being resolved.
An electric dipole p with arbitrary direction and is at distance a from plane infinite conductor at z=0.
Using the image of the dipole
##p=(2pcos\theta \hat{z}+psin\theta \hat{x}##
##p'=(2p'cos\theta \hat{z}-p'sin\theta \hat{x}##

Using the following:##V=\frac{\vec{p'}.\hat{r}}{4\pi\epsilon_0{r}^2}##, i get ## V=\frac{p'(2cos\theta-sin\theta)}{4\pi\epsilon_0{r}^2}## Which i can now write as ##\vec{E}## by symple taking the gradient in spherical coordinates. I get: ##\vec{E}=p'\frac{(2cos\theta-sin\theta)\hat{r}+(2sin\theta+cos\theta)\hat{\theta}}{4\pi\epsilon_0{r}^3}##
Now using one of Maxwell's laws i can get the charge distribution: ##\rho=\epsilon_0\nabla.\vec{E}=\frac{psin\theta}{4\pi{r}^4}## Does it make any sense that this is the result for charge distribution?
Thank you guys, I'm not really sure how to interpret this

Does it make any sense
Not to me. I don't see how it could be radially symmetric.

An electric dipole p with arbitrary direction and is at distance a from plane infinite conductor at z=0.
##p=(2pcos\theta \hat{z}+psin\theta \hat{x}##
I do not understand where that 2 comes from.

I'm sorry, i wanted to edit my post, but somehow i can't :/. That 2 obviously shouldn't be there, it was a mistake when i was writing those in latex. I was doing the math again and i think i got it. If a moderator could delete this thread that would be good. Thank you anyway haruspex.

I'm sorry, i wanted to edit my post, but somehow i can't :/. That 2 obviously shouldn't be there, it was a mistake when i was writing those in latex. I was doing the math again and i think i got it. If a moderator could delete this thread that would be good. Thank you anyway haruspex.
Glad you sorted it out. Don't onow why you could not edit the post... was there no "edit" button?
Forum policy is not to delete threads unless they violate some rule.

## 1. What is a dipole above an infinite conductor?

A dipole above an infinite conductor is a common scenario in electrostatics where a pair of equal and opposite charges are placed at a certain distance above a large conducting plane or sheet that extends infinitely in all directions.

## 2. What is the significance of studying a dipole above an infinite conductor?

Studying a dipole above an infinite conductor allows us to understand the behavior of electric fields and potentials in this common scenario, which can be applied to various real-world situations such as antennas, capacitors, and electrostatic shields.

## 3. How is the electric field and potential calculated for a dipole above an infinite conductor?

The electric field and potential for a dipole above an infinite conductor can be calculated by using the image charge method, where the infinite conductor is replaced by an equivalent image charge with opposite sign placed at a certain distance below the dipole. The resulting electric field and potential can then be calculated using the superposition principle.

## 4. What is the behavior of the electric field and potential in a dipole above an infinite conductor?

In this scenario, the electric field and potential are symmetrically distributed around the dipole, with the electric field lines perpendicular to the infinite conductor and the potential being constant at the surface of the conductor. As the distance from the dipole increases, the electric field and potential decrease according to an inverse square law.

## 5. How does the behavior of the electric field and potential change if the distance between the dipole and infinite conductor is increased or decreased?

If the distance between the dipole and infinite conductor is increased, the electric field and potential decrease, while a decrease in distance results in an increase in the electric field and potential. However, the symmetry of the electric field and potential around the dipole remains the same regardless of the distance.

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