# Why a magnetic flux in closed surface area is always 0?

Why a magnetic flux in closed surface area is always 0?

Apply Lenz' law to a spherical hollow surface, all the charges move to oppose the magnetic field and each other and it all cancels out.

Compare with gravity...

Apply Lenz' law to a spherical hollow surface, all the charges move to oppose the magnetic field and each other and it all cancels out.

Compare with gravity...

Do you have some diagram or picture?

Hmmm dst, can you explain this further? This is very similar to how the Faraday's cage works right?

the E field entering the close surface is equal to the E field exiting the close surface ;)

oops, it should be magnetic flux instead of e field

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Doc Al
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Gauss' Law for Magnetism

Why a magnetic flux in closed surface area is always 0?
This is one of Maxwell's equations. It essentially says that there are no magnetic monopoles (only dipoles, which give no net flux through any surface surrounding them). See: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c2"

Contrast this with Gauss's law for electric fields. No problem getting a non-zero electric flux through a closed surface--just have it enclose a net charge.

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This is one of Maxwell's equations. It essentially says that there are no magnetic monopoles (only dipoles, which give no net flux through any surface surrounding them). See: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/maxeq2.html#c2"

Contrast this with Gauss's law for electric fields. No problem getting a non-zero electric flux through a closed surface--just have it enclose a net charge.
I saw that law, but still can't understand what is happening inside the closed surface.

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0 magnetic flux, is 0 times the magnetic field is perpendicular to the area or what? As I know Gauss' law for Magnetism is different for electric fields. In case of electric fields, it is not zero.

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Doc Al
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The net magnetic flux through a closed surface is zero. Magnetic flux is defined and illustrated here: http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/fluxmg.html" [Broken]

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In the case of STATIONARY fields, the magnetic flux through a closed surface is definitely zero.
And what about non-stationary fields? Is it still zeroing?

PS
I am so lazy to take integral... maybe anybody already knows the answer?

Doc Al
Mentor
In the case of STATIONARY fields, the magnetic flux through a closed surface is definitely zero.
And what about non-stationary fields? Is it still zeroing?
Yep. Maxwell's equations still hold.

Why a magnetic flux in closed surface area is always 0?
Does it help to think about the fact that lines of magnetic flux are always closed loops (since there are no monopoles for them to begin or end on)? You can't draw a closed loop that intersects a closed surface at only one point; it goes in at one point and out at another - i.e. number of "innies" = number of "outies", hence zero net flux.

Does it help to think about the fact that lines of magnetic flux are always closed loops (since there are no monopoles for them to begin or end on)? You can't draw a closed loop that intersects a closed surface at only one point; it goes in at one point and out at another - i.e. number of "innies" = number of "outies", hence zero net flux.

Does it have something with the Faraday's cage?

Does it have something with the Faraday's cage?
Not really - as stated in a previous post, the lines of electric flux do not have to total zero through a closed surface. The Faraday cage has more to do with charges in the cage realigning themselves to cancel the contained field. It works only with an electrically conductive closed surface; it's not true for just any mathematical closed surface, as it is for the case of the magnetic flux through a closed surface.

Not really - as stated in a previous post, the lines of electric flux do not have to total zero through a closed surface. The Faraday cage has more to do with charges in the cage realigning themselves to cancel the contained field. It works only with an electrically conductive closed surface; it's not true for just any mathematical closed surface, as it is for the case of the magnetic flux through a closed surface.
But isn't the magnetic flux, a magnetic field perpendicular to some area? How is possible that the magnetic field is 0, when still it exists?

But isn't the magnetic flux, a magnetic field perpendicular to some area? How is possible that the magnetic field is 0, when still it exists?
You can define a surface perpendicular to the lines of the magnetic field if you want to, but that's not necessary for the statement in question - it's true for any closed surface, no matter how it is oriented.

And no - the magnetic field is not zero, nor is the flux (this was stated in an earlier post - please read them all). It's the net flux, i.e. the sum of all the flux lines across the surface, that is zero. It just means that there is much field "flowing" out of the surface as there is field "flowing" into the surface. Again, it has to do with the closed loops: every one that exits must also reenter.

You can define a surface perpendicular to the lines of the magnetic field if you want to, but that's not necessary for the statement in question - it's true for any closed surface, no matter how it is oriented.

And no - the magnetic field is not zero, nor is the flux (this was stated in an earlier post - please read them all). It's the net flux, i.e. the sum of all the flux lines across the surface, that is zero. It just means that there is much field "flowing" out of the surface as there is field "flowing" into the surface. Again, it has to do with the closed loops: every one that exits must also reenter.
Ok, I understand now. And what happens in the Faraday's cage? Are just the sum of all the flux lines zero?

Ok, I understand now. And what happens in the Faraday's cage? Are just the sum of all the flux lines zero?
Well, that's kind of a funny question, since a Faraday cage relies on the presence of electric charges on the surface, so there will be flux line originating on the surface itself. I guess the correct thing to say, since there are no flux lines in the space inside the surface, is that the flux lines from any external field are exactly cancelled by the flux lines from the rearranged charges on the cage, so you could conclude that the flux is zero everywhere on the surface, not just summed up.

That's my immediate response, anyway. Maybe someone else will disagree ...

Well, that's kind of a funny question, since a Faraday cage relies on the presence of electric charges on the surface, so there will be flux line originating on the surface itself. I guess the correct thing to say, since there are no flux lines in the space inside the surface, is that the flux lines from any external field are exactly cancelled by the flux lines from the rearranged charges on the cage, so you could conclude that the flux is zero everywhere on the surface, not just summed up.

That's my immediate response, anyway. Maybe someone else will disagree ...
And can I ask you another question? How is possible that the field of the permanent magnet is changed (delta B)? Here is the http://hyperphysics.phy-astr.gsu.edu/hbase/electric/farlaw.html#c2"

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Doc Al
Mentor
How is possible that the field of the permanent magnet is changed (delta B)?
The field of the permanent magnet is not being changed. The field (and thus flux) within the conducting loop changes as the magnet is moved.

The field of the permanent magnet is not being changed. The field (and thus flux) within the conducting loop changes as the magnet is moved.
But I think, if I get close permanent magnet (depends on the material), the magnetic domains inside the loop will align, so it will become also permanent magnet. So when I'll return the magnet back, the domains will not align like on the start, right?

Doc Al
Mentor
But I think, if I get close permanent magnet (depends on the material), the magnetic domains inside the loop will align, so it will become also permanent magnet. So when I'll return the magnet back, the domains will not align like on the start, right?
No. Treat the conducting loop as being made from a non-magnetic material, such as copper wire.

No. Treat the conducting loop as being made from a non-magnetic material, such as copper wire.

So, when I put back the magnet, the magnetic domains of the conducting loop will realign, right?

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Doc Al
Mentor
So, when I put back the magnet, the magnetic field of the conducting loop will realign, right?
The only magnetic field contribution from the conducting loop is due to the current flowing through it.

The only magnetic field contribution from the conducting loop is due to the current flowing through it.
Yes, but there are 3 kinds of fields, in this case. B induced, the magnetic field induced due to flowing current, B, the field of the permanent magnet, and delta B, which is actually I think the field inside the coil, but from the spin and orbital momentum of the electrons. So, I think that when I approach permanent magnet, so it will align the domains (temporary), because there is non-magnetic material. But when I get back the permanent magnet, the domains will realign in their first condition. What do you think?