Ampére's law question

[QuantumJG]

hey guys,

I have an ampere's law question (below is the details)

Anyway I thought about it and chose a square as my amperian loop, but, part b isn't a proof and there is no solution so I don't know whether this is right or wrong.

Anyway I determined that:



but I think that may be wrong!

[QuantumJG]

Does anyone know whether I did this right or wrong?

[/0]

How did you choose your rectangle?

I'm just taking punts here, but maybe if you have one side of the rectangle ON the plane of wires (but perpendicular to them), that side will have no field? So then if you pick your opposite side so it's not on the plane and if they are both length L, then

[/tex]\oint B \cdot dl= B L = \mu_0 I_{total}[/tex]

[/tex]I_{total} = InL[/tex]

[/tex]B = \mu_0In[/tex]


When integrating along a loop, does the magnetic field direction matter as long as it's in the same direction as your path along the loop?

If it doesn't matter  then I would try a loop with sides above and below the plane (but perpendicular to the wires). If these sides have length L then









Not sure how correct this is... especially since I would intuitively think the opposite field directions above and below would cancel out...

Actually I'm not quite sure what they want for b)... not very clear

[QuantumJG]

How did you choose your rectangle?

I'm just taking punts here, but maybe if you have one side of the rectangle ON the plane of wires (but perpendicular to them), that side will have no field? So then if you pick your opposite side so it's not on the plane and if they are both length L, then

[/tex]\oint B \cdot dl= B L = \mu_0 I_{total}[/tex]

[/tex]I_{total} = InL[/tex]

[/tex]B = \mu_0In[/tex]

When integrating along a loop, does the magnetic field direction matter as long as it's in the same direction as your path along the loop?

If it doesn't matter  then I would try a loop with sides above and below the plane (but perpendicular to the wires). If these sides have length L then









Not sure how correct this is... especially since I would intuitively think the opposite field directions above and below would cancel out...

Yeah ok I understand what you are saying:

I drew a diagram:

So basically the magnetic fields going perpendicular to the plane are cancelling eachother out, but, wouldn't the magnetic field weaken as you go up higher (i.e. at infinity above the plane would B be the same as on the surface?).

[/0]

Actually I thought the field would be going left on top and right below... (i mean at any distance from the plane)
I don't really know how to explain 'why' the field is constant at any distance from the plane, that's what the derivation says though. I think it might be something similar to how charged plates have the same electric field at any distance.

Hang on i'll do a digram just in case i didn't explain well enough

[QuantumJG]

Actually I thought the field would be going left on top and right below... (i mean at any distance from the plane)
I don't really know how to explain 'why' the field is constant at any distance from the plane, that's what the derivation says though. I think it might be something similar to how charged plates have the same electric field at any distance.

Hang on i'll do a digram just in case i didn't explain well enough

I was just chatting to a friend and he gave the best answer to why.

Basically say we let the height of the loop be larger than l, but, widthwise still l, hence, the current through the loop hasn't changed and the loop no matter how heigh will always have the same magnetic field strength.

i.e. the magnetic field strength is independent on how far away you are from something in this case.