Question

Does the direction of a solenoid matter? Why or why not?

Answer 1

If we turn the solenoide the field should be the same , means direction of the solenoide doesn't matter.

if we consider the solenoide of long length then none segment of solenoide looks identical to segment next to it .The mangnetic field of these sengment should be same .At the middle of solenoide the field does not change from one part to next part this is called translation symmetry . we also have rotational symmetry here. Hence the direction of the solenoid doesn't matter.