Helmholtz coil is named after the German physicist Hermann von Helmholtz. It is comprised of two identical magnetic coils positioned in parallel to each other, and their centers are aligned in the same x-
Helmholtz Coils
The two coaxial coils of equal radii placed at distance equal to the radius of either of the coils and in which same current in same direction is flowing are known as Helmholtz coils.
For these coils $x=\frac{a}{2}, I_{1}=I_{2}=I, a_{1}=a_{2}=a$
The two coils are placed mutually parallel to each other these coils are used to produce a uniform magnetic field. In between two coils along the axis at middle point rate of change of magnetic field is constant so if distance increases from a coil magnetic field decreases but distance from the another coil decreases so magnetic field due to second coil increases and hence the resultant magnetic field produced in the region between two coils remains uniform.
or $\mathrm{B}=0.76 \frac{\mu_{0} n \mathrm{I}}{a} \quad$ or $\mathrm{B}=1.423 \mathrm{B}_{\mathrm{C}}$
(Bc is magnetic field at the centre of a single coil.)\
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