What is the Magnetic Flux Exiting a Cube?

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SUMMARY

The discussion centers on calculating the magnetic flux exiting a cube, specifically using the equation for magnetic flux, which is defined as ∫B dot dA. The calculated magnetic flux for one face of the cube is 0.499 Wb, derived from the magnetic field vector (7.74 ^i + 4 ^j + 3 ^k) T and the area of the face (0.254 m)^2. The net flux for a closed surface is confirmed to be zero, implying that if 0.499 Wb exits from one face, then -0.499 Wb must exit from the other five faces to maintain this balance, consistent with the divergence theorem and the property that magnetic fields are divergence-free.

PREREQUISITES
  • Understanding of magnetic flux and its calculation using integrals.
  • Familiarity with vector calculus, specifically the divergence theorem.
  • Knowledge of magnetic field properties, including the concept of divergence-free fields.
  • Basic proficiency in physics, particularly electromagnetism.
NEXT STEPS
  • Study the divergence theorem in the context of electromagnetism.
  • Explore the implications of magnetic fields being divergence-free.
  • Learn about the relationship between electric charges and magnetic flux.
  • Investigate the differences between conservative and non-conservative fields in physics.
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Students and professionals in physics, particularly those studying electromagnetism, as well as educators looking for clear explanations of magnetic flux concepts and calculations.

4Phreal
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Homework Statement



Here is the prompt: http://imgur.com/FTFz0fZ


Homework Equations



Magnetic flux = ∫B dot dA

Net Flux for closed surface = 0


The Attempt at a Solution



For part a:
magnetic flux = (7.74 ^i + 4 ^j + 3 ^k)T * (0.254 m)^2 ^i
= 7.74 T * (0.254m)^2 m
= 0.499 Wb

For part b:
I'm not really sure. I know that the net flux for a closed surface is 0, so does that mean if 0.499 Wb is exiting from one face that -0.499 Wb would be exiting from the other 5 to make it 0?
= -0.499 Wb??
 
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Assuming the numerical values are correctly computed, what you have done seems reasonable.
 
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Well the total flux would be the sum of the flux from all 6 sides.

Just out of curiosity is this a webassign problem?
 
BiGyElLoWhAt said:
Well the total flux would be the sum of the flux from all 6 sides.

And magnetic fields are conservative, which means that the total flux is zero. This is the property he is using...
 
I understand that. I'm just saying he could always check it if he was doubtful, which is what I got out of the OP.
 
It's not that magnetic fields are conservative. Electrostatic fields are conservative, but the net flux emanating from a volume is zero if and only if there is no charge inside that volume.

In fact, there is no meaning to calling a magnetic field conservative since moving a charge around a mag. field results in zero work no matter where the start and end of the path is. In a conservative field, the force is derivable from the gradient of a scalar, which is not the case for a mag. field.

(A few authors do consider the mag. field conservative since the circulation is zero but that is far-fetched.)

The property he is invoking is ∇*B = 0 i.e. there are no isolated poles in a mag. field that can be stuck inside a given volume. So by the divergence theorem the total mag. flux out of any closed surface = 0.
 
Last edited:
4Phreal said:

Homework Statement



Here is the prompt: http://imgur.com/FTFz0fZ


Homework Equations



Magnetic flux = ∫B dot dA

Net Flux for closed surface = 0


The Attempt at a Solution



For part a:
magnetic flux = (7.74 ^i + 4 ^j + 3 ^k)T * (0.254 m)^2 ^i
= 7.74 T * (0.254m)^2 m
= 0.499 Wb

For part b:
I'm not really sure. I know that the net flux for a closed surface is 0, so does that mean if 0.499 Wb is exiting from one face that -0.499 Wb would be exiting from the other 5 to make it 0?
= -0.499 Wb??

Right.
 
Indeed, brain freeze. What I meant to say was "divergence free".
 

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