Magnetic field of plane current/solenoid (Griffiths ex. 5.8 and 5.9)

[wizzart]

Time for me to feel stupid again:

In Griffiths' introduction to electro dynamics examples 5.8 and 5.9 the magnetic fields of plane currents and solenoids are discussed. In both, certain components of the magnetic fields are said to be zero based on symmetry and current reversal arguments. I'm a believer, just don't understand WHY.

For those who don't own Griffiths:
-Why is the Z-component of a current in the xy plane zero (i.o.w. why can't it change if the direction of the current is reversed).
-Why is there no radial component of the field of a solenoid with a circumferential surface current?

Thanks in advance.

 

[wizzart]

Think I figured it out. For instance, in the case of the solenoid: if instead of reversing the current or rotating the solenoid 180 deg. I stand on my head and look at the magnetic field, I should still see the same field...

If this is correct, I apologize for the forum pollution.