Helmholtz Coils

UTD physics $($C$)$ Fall $2024$

$2.$ A coil is made up of $N$ closely packed loops. The magnetic field on the axis of the coil has the components,

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

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