What is the Magnetic Flux Exiting a Cube?

[4Phreal]

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??

 

[Orodruin]

Assuming the numerical values are correctly computed, what you have done seems reasonable.

 

[BiGyElLoWhAt]

Well the total flux would be the sum of the flux from all 6 sides.

Just out of curiosity is this a webassign problem?

 

[Orodruin]

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...

 

[BiGyElLoWhAt]

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.

 

[rude man]

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.

 

[rude man]

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.

 

[Orodruin]

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