# Electric field of a point charge

• willDavidson
In summary, a point charge is a theoretical concept that can be described as a charge density consisting of a Dirac delta function. This recovers the Coulomb law and can be converted to Coulomb's law by using the divergence theorem and choosing a spherical surface. It is infinitely small and can be represented by a three dimensional Dirac delta function.
willDavidson
TL;DR Summary
I am trying to understand what a point charge is.
I am trying to understand what a point charge is. Is it just an electron? Or is it just an idea?

A point charge ##q## at position ##\vec{r}_0## is described by a charge density consisting of a Dirac delta function, ##\rho(\vec{r}) = q\delta^{3}(\vec{r} - \vec{r}_0)##.

Edit: N.B. you can also check that this recovers the Coulomb law, i.e. from Maxwell I,$$\nabla \cdot \vec{E} = \frac{\rho}{\varepsilon_0}$$Perform a volume integral over a region ##\Omega## on both sides, and then use the divergence theorem on the LHS,$$\int_{\partial \Omega} \vec{E} \cdot d\vec{S} = \frac{1}{\varepsilon_0} \int_{\Omega} q\delta^3(\vec{r} - \vec{r}_0) dV = \frac{q}{\varepsilon_0}$$That's Gauss' law in integral form, which you can convert to Coulomb's law by choosing ##\partial \Omega## to be a spherical surface concentric with the point charge, of radius ##R##, $$4\pi R^2 E_r = \frac{q}{\varepsilon_0} \implies E_r = \frac{q}{4\pi \varepsilon_0 R^2}$$

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It's just a theoretical concept. It's infinitely small. There's not much more than that to it. And yes, if you want to describe it as a charge distribution you'd use a three dimensional dirac delta function for it.

## 1. What is the formula for calculating the electric field of a point charge?

The formula for calculating the electric field of a point charge is given by E = k*q/r^2, where k is the Coulomb's constant, q is the magnitude of the charge, and r is the distance from the point charge.

## 2. How does the electric field of a point charge change with distance?

The electric field of a point charge follows an inverse square law, meaning that it decreases with the square of the distance from the point charge. This means that the further away you are from the point charge, the weaker the electric field will be.

## 3. What is the direction of the electric field of a point charge?

The direction of the electric field of a point charge is always away from a positive charge and towards a negative charge. This is because electric field lines represent the direction of the force that a positive test charge would experience in the presence of the point charge.

## 4. Can the electric field of a point charge be negative?

Yes, the electric field of a point charge can be negative. This would occur if the point charge is negative, as the direction of the electric field would be towards the negative charge.

## 5. How does the electric field of a point charge compare to that of a dipole?

The electric field of a point charge is a radial field, meaning that the field lines extend outwards in all directions. In contrast, the electric field of a dipole has a more complex shape, with field lines that extend from the positive charge to the negative charge. Additionally, the electric field of a dipole is typically stronger near the charges and decreases more rapidly with distance compared to a point charge.

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