Magnetic Field due to a unifrom thin current sheet of infinite extent

[Cummings]

There is a uniform thin current sheet of infinite extent in the x,y plane.

Assuming the magnetic field is only a funtion z, perpendicular to the plane and that the magnetic field direction is parallel to the plane and perpendicular to the current direction (which is in the positive x direction)

I am asked to find an equation for the magnetic field due to the current plane using the integral form of Gauss law.

Now, all we have been taught is the magnetic field due to a current in an infinatly long wire. So, what wire would simulate this plane? I am guessing one with an infinite radius. As the magnetic field from an infinatly long straight wire does not depend on the radius, i figured that the magnetic field due to the plane is zero. Is this right? I got it using the below working.

B * 2Pi * radius of point to be measured = uI
B = uI/(2Pi * radius of point)

if the radius of the wire is infinant, then the radius of the point to be measured (in z direction) must also be infinant. This would make the magnetic field reduce to zero.

Are we on the right track? If you can't understand my working, just tell me if the magnetic field due to a infinant current plane is zero or not.

Thanks,
Cummings

 

[whozum]

Well firstly, its 'infinite'.

Second, wherever there is a moving charge, there is a magnetic field associated with that charge.

You can use the 'pillbox' Gaussian surface to find the magnetic field here, you should find this in your textbook. If it isn't under the magnetics section, try the E-field section, same basic principle.

 

[Cummings]

we are using a university made textbook and so do not have access to anything else.

The exact question is as follows

Use Amperes law in integral form for a static field to find an espression for the magnetic field due to a uniform thin current sheet of infinant extent in the x-y plane with surface current density J in the positive x direction. (Assume that the field strength is a function only of the perpendicular surface, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

 

[OlderDan]

we are using a university made textbook and so do not have access to anything else.

The exact question is as follows

Use Amperes law in integral form for a static field to find an espression for the magnetic field due to a uniform thin current sheet of infinant extent in the x-y plane with surface current density J in the positive x direction. (Assume that the field strength is a function only of the perpendicular surface, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

I think this is supposed to say

(Assume that the field strength is a function only of the perpendicular distance, z, from the sheet and that the field direction is parallel to the sheet and perpendicular to the current direction.

Given the stated symmetry, the integral form of Ampere's law involves a very simple calculation. Think about the integral for a rectangular loop cutting through the sheet.

http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/amplaw.html