Two identical coaxial coils, each of N turns and radius b, are separated by a distanced, a...

Two identical coaxial coils, each of N turns and radius b, are separated by a distanced, as depicted in Fig. 6- 39. A current I flows in each coil in the same direction.

a) Find the magnetic flux density B = axBx at a point midway between the coils.

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b) Show that dBx/dx vanishes at the midpoint.

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c) Find the relation between b and d such that d2Bx/dx2 also vanishes at the midpoint.

Such a pair of coils are used to obtain an approximately uniform magnetic field in the midpoint region. They are known as Helmholtz coils.

Figure: Helmholtz coils