# Help with linear charge density and flux

• artsakh
In summary, the problem involves finding the electric flux through a closed spherical surface centered at the origin, with a uniform linear charge density of -2 nC/m on the y-axis and point charges of 8 nC and -4 nC at specific points. The charge outside the sphere does not affect the flux. The correct answer can be found by calculating the total charge inside the sphere, which includes the charge density and the 8 nC point charge.
artsakh

## Homework Statement

The y-axis carries a uniform linear charge density of -2 nC/m, and there is a 8 nC point charge
at the point (3 cm, 0 cm, 0 cm) as well as a -4 nC point charge at the point (-8 cm, 0 cm, 0 cm).
What is the electric flux through a closed spherical surface of radius 4 cm centered at the origin?

## Homework Equations

I know that flux is 4πkQin or Qin0, i don't understand where the linear charge density comes in. I know that the 8nC charge would be inside the sphere.

## The Attempt at a Solution

I tried adding the linear charge density and the 8nC charge and putting it through that formula but i don't understand how the -4nC charge affects the flux, or how to factor it in.

Any help would be greatly appreciated

Last edited:
The charge outside the sphere doesn't affect the flux, correct? when adding the charges inside the sphere, -2 and 8, which gives 6nC, and putting it through the formula, 4πkQin, i get 678.58, but the correct answer is 886Nm2/C

You are correct that the charge outside the sphere has no influence.
You have made a mistake in determining the charges inside. While there is one charge of 8nC, the 2nC/m is a charge density, not a charge itself.
You need to calculate the amount of charge within the sphere given this charge density, and the radius of the sphere. How might that be accomplished?

well i have the equation E = 2kλ/r. E = k8nC/(.08)2?? but how does that help??

Just think about the charge on the y-axis for a moment.
It has a charge density -2nC/m. The sphere is radius 0.04m, so what is the total charge (on the y-axis) inside the sphere?

im not sure. i don't see how its related at all, i mean besides a volume-density relation

The charge density means that for every metre on the y-axis, there are -2nC of charge present. There is 0.08m of the y-axis within the sphere.
Since charge density = charge/length, you can rearrange this equation to give the charge on the y-axis contained within the sphere.

## 1. What is linear charge density?

Linear charge density, denoted by λ, is a measure of the amount of electric charge per unit length along a charged line. It is expressed in units of coulombs per meter (C/m).

## 2. How is linear charge density calculated?

Linear charge density is calculated by dividing the total charge (Q) by the length (L) of the charged line, using the formula λ = Q/L. It is important to ensure that the units of charge and length are consistent.

## 3. What is electric flux?

Electric flux, denoted by Φ, is a measure of the amount of electric field passing through a given surface. It is a scalar quantity and is expressed in units of volts per meter squared (V/m²).

## 4. How is electric flux related to linear charge density?

The electric flux through a surface is directly proportional to the linear charge density of a charged line. This relationship is expressed by the formula Φ = λL, where L is the length of the surface intersecting the charged line.

## 5. Can linear charge density and electric flux be negative?

Yes, both linear charge density and electric flux can be negative. This indicates that the electric charge or electric field is directed in the opposite direction of the chosen coordinate system. It is important to pay attention to the sign conventions when using these quantities in calculations.

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