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If we put the loop outside the coil it can be established that B=0

If we use the loop to enclose the coil and we apply Ampere's Law we get that [itex]\vec{B}=\mu_0 NI \mathbf{\hat{z}}[/itex]

apparently this means that the field is [itex]\mu_0 NI \mathbf{\hat{z}} \forall r < a[/itex] and [itex]0 \forall r>a[/itex]

two questions:

(i)why, if we take an amperian loop INSIDE the coil (i.e. not enclosing any current, doesn't the field =0 by ampere's law?

(ii) what is the field at r=a?

thanks