Magnetic Flux Exiting a Cube

1. Jul 9, 2014

4Phreal

1. The problem statement, all variables and given/known data

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

2. Relevant equations

Magnetic flux = ∫B dot dA

Net Flux for closed surface = 0

3. 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??

2. Jul 9, 2014

Orodruin

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

3. Jul 9, 2014

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?

4. Jul 9, 2014

Orodruin

Staff Emeritus
And magnetic fields are conservative, which means that the total flux is zero. This is the property he is using...

5. Jul 9, 2014

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.

6. Jul 10, 2014

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.

Last edited: Jul 10, 2014
7. Jul 10, 2014

rude man

Right.

8. Jul 10, 2014

Orodruin

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

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