$B_x=\frac{{}_0\text{I}}{2}\frac{N{a}^2}{(a^2+x^2{)}^{\frac{3}{2}}},B_y=0=B_z.$

This expression has many similarities to the expression for a single circular loop. Why is there a factor $($f $N$ when we generalize to a coil with $N$ circular loops? $($Hint: just saying that there are $N$ loops in the coil isn't enough.$)$

The hital magnue hund B is the product of the # of loops N & the mynce fiuld dive to a singlelloop$.$

$3.$ Will the axial component of the field caused by $N$ loops be $B_x=\frac{{}_0\text{I}}{2}\frac{N{a}^2}{(a^2+x^2{)}^{\frac{3}{2}}}$ if the loops are loosely packed and so don't have their centers near $x=0?$ Explain your answer.