Diraction of Magnetic Field Due to an Infinitely Large Current

[pardesi]

well i saw a proof in griffith about the diraction of magnetic field due to an infinitely large steady current carrying plate in x direction .well i could argue on the normal basis of an current element being at equal distances and component cancellingout...that the field has to be in y direction.
but then he gave a beautiful proof arguing on the line that if there were field in z direction then by biot savrt law reversing current would reverse it's direction
upto this everything was ok
then he writes but the field in z direction can't possibly depend on current direction in xy plane
why is this?

 

[ZapperZ]

well i saw a proof in griffith about the diraction of magnetic field due to an infinitely large steady current carrying plate in x direction .well i could argue on the normal basis of an current element being at equal distances and component cancellingout...that the field has to be in y direction.
but then he gave a beautiful proof arguing on the line that if there were field in z direction then by biot savrt law reversing current would reverse it's direction
upto this everything was ok
then he writes but the field in z direction can't possibly depend on current direction in xy plane
why is this?

You missed an important description to the problem. Since you have a plane, you did not tell us in which plane it is. All you did was gave the direction of the current.

From reading the rest of your post, I am guessing that this plane is in the xy-plane, with the current in the x-direction as stated. If this is true, then yes, by symmetry argument, the z-direction would not change if you change the direction of the current.

Think of what happens when, instead, you have the same plane, but now you have a uniform charge. The charge distribution has a translational symmetry in the xy plane, and it has reflection symmetry along a plane perpendicular to it. The field must have the same symmetry, and that's why you get an E-field along the z-direction.

Apply that to your problem. While the plane still has translational symmetry, an inversion of the current (or doing a reflection along the same plane) will now change the direction of the current. The field generated must also have the same symmetry.

Zz.

 

[pardesi]

sorry i didn't metion that the current was in xy plane but can u explain why the change in current direction doesn't affetc the magnetic fiels along z axis

 

[ZapperZ]

I thought I just did?!

Zz.

 

[pardesi]

well if i am right u have written tht effectively if we change the direction of current by reflection then the field direction should also change then what...