A Helmholtz coil has a pair of loops, each with $N$ turns and radius $R$ . They are placed coaxially at distance $R$ and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P,$ midway between the centres $A$ and $C,$ is given by [Refer to figure given below]:

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Magnetic field at point P, due to both coils, B p = 2 μ 0 N I R 2 2 R 2 + R 2 4 3 / 2 = μ 0 N I R 2 5 3 / 2 8 R 3 = 8 N μ 0 I 5 3 / 2 R .

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