Closed Surface Flux: Is It Always Zero?

[limonade]

1. The problem statement, all variables and given/known dat
Say I have a closed surface

is the flux across this closed surface only zero if the force originates from inside the surface?

What about if it originates outside the closed surface and can penetrate through the closed surface, would it still be zero?

Is it only zero for a magnetic force?

What about an electrical flux?

Homework Equations

The Attempt at a Solution

 

[Dick]

1. The problem statement, all variables and given/known dat
Say I have a closed surface

is the flux across this closed surface only zero if the force originates from inside the surface?

What about if it originates outside and can penetrate through the closed surface, would it still be zero?

Is it only zero for a magnetic force?

What about an electrical flux?

Homework Equations

The Attempt at a Solution

I'm not sure exactly what you mean by 'originates from'. Define it more clearly and use vector calculus ideas and Maxwell's equations if you talking about electromagnetism.

 

[limonade]

What I mean is what if the force originates from outside the closed surface and passes through it, assuming the surface is made of a penetrable material.

 

[Dick]

What I mean is what if the force originates from outside the closed surface and passes through it, assuming the surface is made of a penetrable material.

Depends on what kind of field you are talking about. Sounds you are talking about sources of electric and magnetic fields. Formulate the question in terms of those, like if you have a charge outside the sphere, does it create a net flux? What about inside? Use theorems!

 

[rude man]

1. The problem statement, all variables and given/known dat
Say I have a closed surface

is the flux across this closed surface only zero if the force originates from inside the surface?

What about if it originates outside the closed surface and can penetrate through the closed surface, would it still be zero?

Is it only zero for a magnetic force?

What about an electrical flux?

For electrostatic flux, yes, the surface integral of flux is zero if and only if there is no net charge inside the closed surface. That's what Gauss's theorem says. Charges external to the closed surface generate flux that goes in & out of the closed surface but their net contribution to flux = ∫∫E*dA is zero.

For magnetic fields of any kind, div B = 0 always so the integral of magnetic flux over any closed surface is always = 0.

cf. the Divergence theorem.

Homework Equations

The Attempt at a Solution

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