A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by \frac{N}{12} \textrm{ } \left(\mu\right)

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A cylindrical cavity of diameter a exists inside a cylinder of diameter 2a as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density J flows along the length. If the magnitude of the magnetic field at the point P is given by $\frac{N}{12} μ_{0} aJ$ , then the value of N is

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$B_{P} = \frac{μ_{0} Ja}{2} - \frac{μ_{0} J π {(\frac{a}{2})}^{2}}{2 π \frac{3 a}{2}} = \frac{μ_{0} Ja}{2} [1 - \frac{1}{6}] = \frac{5 μ_{0} Ja}{12} ∴ N = 5$

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