# Volume charge density w/o surface charge density

• vikasagartha
In summary, the conversation discusses the concept of electric field in uniform, circular charge density. The equations for the electric fields inside and outside the volume are given, and it is noted that the electric field is continuous at a certain radius. The confusion arises from the absence of a surface charge, but it is realized that the mistake was due to the direction of the electric field.
vikasagartha
Im confused by a concept i have run across in Griffiths electrodynamics.

$E_{out} - E_{in} = \frac{\sigma_{free}}{\epsilon_0}$

However, in the case of a uniform, circular charge density,
$\vec{E_{in}} = \frac{\rho r}{3\epsilon_0}\hat{r}$
$\vec{E_{out}} = \frac{\rho R^3}{3\epsilon_0 r^2}\hat{r}$

But this electric field is continuous @ r=R. If a volume has a charge density, doesn't it have to have some sort of a surface charge? How can there be no surface charge?

Silly question. Realized my mistake. Sorry. I forgot that the normal to the electric field is in opposite directions when drawing a 'pillbox.' So sorry.

Last edited:

## 1. What is volume charge density?

Volume charge density is a measure of the electric charge per unit volume of a given material or region. It is typically denoted by the Greek letter "rho" (ρ) and has units of coulombs per cubic meter (C/m³).

## 2. How is volume charge density different from surface charge density?

Volume charge density refers to the charge contained within a three-dimensional volume, while surface charge density refers to the charge per unit area on a two-dimensional surface. In other words, volume charge density considers the charge spread out in all directions, while surface charge density only considers the charge on a flat surface.

## 3. What is the relationship between volume charge density and electric potential?

The electric potential at a point in a material is directly proportional to the volume charge density at that point. This means that as the volume charge density increases, the electric potential also increases, and vice versa. This relationship is described by the equation V = ρ/ε, where V is the electric potential, ρ is the volume charge density, and ε is the permittivity of the material.

## 4. How is volume charge density measured?

Volume charge density can be measured using various techniques, such as Coulomb's law, Gauss's law, and capacitance measurements. Coulomb's law involves using a charged object to exert a force on a test charge, while Gauss's law uses the total electric flux through a closed surface to calculate the charge enclosed within that surface. Capacitance measurements involve determining the amount of charge that can be stored on a given capacitor at a certain voltage.

## 5. What are some real-world applications of volume charge density?

Volume charge density is a fundamental concept in electromagnetism and has many practical applications. It is used in the design of electronic circuits, the development of energy storage devices, and the analysis of lightning strikes. It is also an important factor in the behavior of materials in electric and magnetic fields, and plays a role in processes such as electroplating and electrophoresis.

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