# Why do charges outside surface create no net flux?

• yosimba2000
In summary: The size of the Gaussian surface can be considered constant. The Gaussian surface itself is arbitrary and how it is drawn and is not constrained by the behavior of the electric field. Although picking a surface with identical symmetry to the field can drastically simplify the problem.
yosimba2000
Why do charges outside the surface contribute 0 net flux? The book I'm reading says it's because the flux entering the surface cancels out with the flux exiting the surface. But that means E dot Area must be exactly the same magnitude when entering and exiting to cancel out.

But we know E-field decreases by factor of R2, so as you increase in distance, area must increase by R2 in order to maintain the same magnitude of flux.

But what about in this situation? https://imgur.com/a/c2KS8

The areas penetrated by the E-Field have the same magnitude, but the E-fields are of different strength because E-Fields decrease by R2. So E dot A is different at each area, so flux in this situation cannot be 0.

yosimba2000 said:
But what about in this situation? https://imgur.com/a/c2KS8
Flux also leaves the sides.

Sometimes thinking about lines of flux helps. If there is no charge in the surface then no lines start or stop inside the surface. Therefore, every line which goes in one side must come out somewhere else.

yosimba2000 said:
But that means E dot Area must be exactly the same magnitude when entering and exiting to cancel out.
It means that the integral of ##\mathbf{E}\cdot\mathbf{a}## must be zero
$$\oint\mathbf{E}\cdot d\mathbf{a}=0$$
yosimba2000 said:
But we know E-field decreases by factor of R2, so as you increase in distance, area must increase by R2 in order to maintain the same magnitude of flux.
The size of the Gaussian surface can be considered constant. The Gaussian surface itself is arbitrary and how it is drawn and is not constrained by the behavior of the electric field. Although picking a surface with identical symmetry to the field can drastically simplify the problem.
yosimba2000 said:
The areas penetrated by the E-Field have the same magnitude, but the E-fields are of different strength because E-Fields decrease by R2. So E dot A is different at each area, so flux in this situation cannot be 0.
You forgot about the flux through the sides and the flux through the ends is not correct. The total flux is zero if you find it correctly.

Dale said:
Flux also leaves the sides.

Sometimes thinking about lines of flux helps. If there is no charge in the surface then no lines start or stop inside the surface. Therefore, every line which goes in one side must come out somewhere else.

But the field strength when the line enters is stronger than when the field line leaves. So still, the areas must somehow compensate for this, right?

yosimba2000 said:
But the field strength when the line enters is stronger than when the field line leaves. So still, the areas must somehow compensate for this, right?
Yes, but there is more area over which the field lines are leaving.

yosimba2000 said:
But the field strength when the line enters is stronger than when the field line leaves. So still, the areas must somehow compensate for this, right?
The field strength is proportional to the spacing of the lines. So it automatically ensures that as the field gets weaker it covers a larger area.

## 1. Why do charges outside surface create no net flux?

Charges outside the surface create no net flux because the electric field lines produced by the charges cancel each other out. This means that the electric field at any point outside the surface is equal in magnitude and opposite in direction, resulting in a net flux of zero.

## 2. How does the electric field outside a charged surface affect the net flux?

The electric field outside a charged surface has a significant impact on the net flux. If the surface has a uniform charge distribution, the electric field outside the surface will be equal in magnitude and opposite in direction, resulting in a net flux of zero. However, if the surface has a non-uniform charge distribution, the electric field outside the surface may not completely cancel out, resulting in a non-zero net flux.

## 3. What is the significance of net flux in relation to charges outside a surface?

The net flux is a measure of the total electric field passing through a surface. In the case of charges outside a surface, a net flux of zero means that the electric field is balanced and there is no overall movement of electric charge across the surface. This is important in understanding the behavior of charges and electric fields in a given system.

## 4. Can charges outside a surface ever create a net flux?

No, charges outside a surface can never create a net flux. This is because the electric field lines produced by the charges always cancel each other out, resulting in a net flux of zero. However, charges inside the surface or on the surface itself can create a non-zero net flux.

## 5. How does the shape of a charged surface affect the net flux created by charges outside the surface?

The shape of a charged surface can impact the net flux created by charges outside the surface. If the surface is curved or has a non-uniform charge distribution, the electric field outside the surface may not completely cancel out, resulting in a non-zero net flux. However, if the surface is flat and has a uniform charge distribution, the electric field outside the surface will cancel out, resulting in a net flux of zero.

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