# Force on a charge from an induced dipole

• Yitzach
In summary, the force of attraction between a point charge q and a neutral atom with polarizability α at a large distance r is given by: F = -αq^2 / 8π^2ε0r^5 in the direction of the negative unit vector r. This may seem unexpected because the force points towards the origin, but it is correct based on the equations for a monopole and dipole.
Yitzach

## Homework Statement

A point charge q is situated a large distance r from a neutral atom of polarizability $$\alpha$$. Find the force of attraction between them.

## Homework Equations

$$\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+\sin\theta\hat{\theta})$$
$$\vec{p}=\alpha\vec{E}$$

## The Attempt at a Solution

$$\vec{E}_{mono}(r)=\frac{q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{p}=\alpha\vec{E}$$
$$\vec{p}=\frac{\alpha q}{4\pi\epsilon_0r^2}\hat{r}$$
$$\vec{E}_{dip}(r,\theta)=\frac{p}{4\pi\epsilon_0r^3}(2\cos\theta\hat{r}+\sin\theta\hat{\theta})$$
$$\vec{E}_{dip}(r,\pi)=\frac{\alpha q}{16\pi^2\epsilon^2_0r^5}(-2\hat{r})$$
$$\vec{E}_{dip}(r,\pi)=-\frac{\alpha q}{8\pi^2\epsilon^2_0r^5}\hat{r}$$
$$\vec{F}=q\vec{E}$$
$$\vec{F}=-\frac{\alpha q^2}{8\pi^2\epsilon^2_0r^5}\hat{r}$$

The result I got was unexpected because that is a repulsive force.
Do I need to go about a longer way or did I mess it up somewhere?

Last edited:
Why do you say that the force is not attractive? It points in the negative ##\hat r## direction, i.e. towards the origin where presumably you put the monopole.

## What is "force on a charge from an induced dipole"?

"Force on a charge from an induced dipole" refers to the force experienced by a charged particle when it interacts with an electric dipole that has been induced in a nearby object.

## What causes an induced dipole?

An induced dipole is caused by the presence of an electric field. When an electric field is applied to a neutral object, the charges within the object will redistribute, resulting in a separation of positive and negative charges and the creation of an induced dipole.

## How does an induced dipole affect the force on a charged particle?

An induced dipole creates a non-uniform electric field, which exerts a force on a charged particle within its vicinity. This force can either attract or repel the charged particle, depending on the orientation of the dipole and the charge of the particle.

## Can the strength of the force on a charged particle from an induced dipole be calculated?

Yes, the strength of the force can be calculated using the equation F = qE, where F is the force, q is the charge of the particle, and E is the electric field strength of the induced dipole.

## What are some real-world examples of the force on a charged particle from an induced dipole?

Some examples include the way water molecules interact with charged ions in a solution, the way charged particles are attracted to a charged balloon, and the way dust particles become electrically charged when rubbed against a surface.

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