# Charge enclosed in uniform electric field

• yeahhyeahyeah
In summary, the problem involves a cube with a corner at the origin and 1m sides extending in the positive x, y, and z directions. The electric field of 3.00 i + 2.5 j passes through the space. Using Gauss' law, we can determine that the charge enclosed by the cube is 0 since the dot products of the faces cancel out. This is because the electric field is uniform across the space.
yeahhyeahyeah
1b]1. Homework Statement

A cube oriented so that its corner lies on the origin and it extends positive 1m in the x, y, and z direction. An electric field of 3.00 i + 2.5 j passes through this space. What is the charge enclosed by the cube?

## The Attempt at a Solution

Gauss' law is
integr(E . dA) = Q/epsilon

since the surface is of a cube, you can add the dot product of E and dA for every face except for the one lying in the x-y plane because there is no 'k' component of the E field.
The dot products of the faces cancel out though
So the the total charge enclosed is 0
is that right?

If the electric field is uniform across the space the cube is in, then you are right that there is no charge inside, because for there to be a charge inside there would have to be a net non-zero flux through all of the faces of the cube.

Yes, that is correct. Since the cube is oriented in such a way that one of its faces is parallel to the x-y plane, the electric field passing through that face (and the corresponding dot product) will be zero. Therefore, the total charge enclosed by the cube will also be zero. This is because Gauss' law states that the integral of the electric field over a closed surface is equal to the total charge enclosed by that surface divided by the permittivity of the medium. In this case, since the integral is zero, the total charge enclosed must also be zero.

## 1. What is the definition of "charge enclosed" in a uniform electric field?

The charge enclosed in a uniform electric field refers to the total amount of electric charge that is included within a specific region or surface in the field. This includes any charges that are both inside and on the boundary of the region.

## 2. How is the charge enclosed in a uniform electric field calculated?

To calculate the charge enclosed in a uniform electric field, you need to find the total flux passing through a closed surface that encloses the region of interest. This can be done using Gauss's Law, which states that the flux through a closed surface is equal to the total enclosed charge divided by the permittivity of the medium.

## 3. Can the charge enclosed in a uniform electric field be negative?

Yes, the charge enclosed in a uniform electric field can be negative. This can occur if there are more negative charges than positive charges enclosed within the region of interest. In this case, the total charge enclosed would be negative, indicating a net negative charge within the region.

## 4. How does the charge enclosed affect the electric field within the region?

The charge enclosed has a direct effect on the strength of the electric field within the region. According to Gauss's Law, the electric field is directly proportional to the total charge enclosed. This means that as the charge enclosed increases, the electric field strength also increases.

## 5. Is the charge enclosed in a uniform electric field always constant?

No, the charge enclosed in a uniform electric field is not always constant. It can vary depending on the region of interest and the distribution of charges within it. In some cases, the charge enclosed may also change if the electric field itself changes, as this can affect the flux through the closed surface.

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