# Flux of Electric field through sphere

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In summary, Gauss's law states that the electric flux through a closed surface is only affected by the charges enclosed by the surface, not by charges outside of it. This is because charges act as sources or sinks of electric flux, and if there are no sources or sinks enclosed by the surface, the net flux through the surface must be zero. This understanding is essential for solving problems involving electric flux and Gauss's law.
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Homework Statement
What is the flux of electric field through sphere with charges inside and outside of the sphere?
Relevant Equations
Electric field flux = Q/ e0
My attempt: We have 3 charges inside 2 +ve and 1 -ve so i just added them up. 4 + 5 +(-7) = 2q
Then there is a -5q charge outside the sphere. I did 2q + (-5q)= -3q . The electric field flux formula is Flux= q/ E0 . So i got -3q/E0 which is obviously wrong : ) . After quick googling , I discovered that the electric flux through a sphere is only dependent on charges enclosed by the sphere , charges outside don't affect electric flux through sphere. Is it correct and why it is the case? I am not familiar with Gauss' law so how do i get started. Thank you

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Tesla In Person said:
After quick googling , I discovered that the electric flux through a sphere is only dependent on charges enclosed by the sphere , charges outside don't affect electric flux through sphere. Is it correct and why it is the case?
That is Gauss’ law.

The sources of electric flux are charges. Think of them as sources (positive) and sinks (negative) of water. If a closed surfaces encloses source, water comes out of the surface at every point on it. Likewise, if a sink is enclosed, water goes into the surface at every point on it. If you have a combination of sources and sinks you need to add all the positives and negatives and see what the net is.

Now if a source is outside the surface and there are no sources or sinks enclosed by the surface, what goes into it through the side closer to the source must come out the other side. You put all this together and you have an intuitive understanding of Gauss's law.

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## 1. What is the definition of flux of electric field through a sphere?

The flux of electric field through a sphere is a measure of the total electric field passing through the surface of a sphere. It is given by the integral of the electric field over the surface area of the sphere.

## 2. How is the flux of electric field through a sphere calculated?

The flux of electric field through a sphere is calculated using the formula Φ = E x A x cosθ, where Φ is the flux, E is the electric field, A is the surface area of the sphere, and θ is the angle between the electric field and the normal vector to the surface.

## 3. What is the unit of measurement for flux of electric field through a sphere?

The unit of measurement for flux of electric field through a sphere is volt-meters (V-m) or newton-meters squared per coulomb (N-m²/C).

## 4. How does the flux of electric field through a sphere relate to Gauss's law?

Gauss's law states that the flux of electric field through a closed surface is equal to the charge enclosed by that surface divided by the permittivity of free space. This can be applied to a sphere by considering the sphere as a closed surface and the charge enclosed as the charge at the center of the sphere.

## 5. What factors affect the flux of electric field through a sphere?

The flux of electric field through a sphere is affected by the magnitude and direction of the electric field, the surface area of the sphere, and the angle between the electric field and the normal vector to the surface. It is also affected by the charge enclosed within the sphere and the permittivity of free space.

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