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 $\mathit{A}$ and $C,$ is given by [Refer to figure given below]:

• A

  $\frac{8N{\mu }_{0}I}{5^{1/2}R}$
• B

  $\frac{4N{\mu }_{0}I}{5^{3/2}R}$
• C

  $\frac{4N{\mu }_{0}I}{5^{1/2}R}$
• Correct answer
  D

  $\frac{8N{\mu }_{0}I}{5^{3/2}R}$

Hence, the correct answer is option: 'D'.