$\begin {array} {1 1} (a)\;2.67 \times 10^{-7} \hat k & \quad (b)\;1.33 \times 10^{-7} \hat k \\ (c)\;-2.67 \times 10^{-7} \hat k & \quad (d)\;-1.33 \times 10^{-7} \hat k \end {array}$

As may be clear from the situation, the magnetic field at the origin can be represented as a difference of two geometric series

$ \overrightarrow B = \large\frac{\mu_0}{2 \pi } $$\hat k \bigg[ \bigg( \large\frac{1}{1} + \large\frac{1}{4}+ \large\frac{1}{16} +....\bigg) - \bigg( \large\frac{1}{2} + \large\frac{1}{8}+....\bigg) \bigg]$$ \large\frac{2}{3}$$ \large\frac{\mu_0}{2 \pi}$

$ = 1.33 \times 10^{-7} \hat k$

Ans : (b)

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