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A long cylinder conductor of radius 2R having cylindrical cavity of diameter 2R throughout its length is lying with its axis of cavity and axis of cylinder is R. A constant current I is passed through the cylinder along its length in the positive $\otimes$ direction. The magnetic field at A is $\frac{μ_{0} I}{P π R}$ then value of P is _______________.

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answer is 6.

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Detailed Solution

$I_{1} = \frac{I}{π [(2 R^{2}) - R^{2}]} \cdot π R^{2} = \frac{I}{3}$

$B \cdot 2 π R = μ_{0} . I_{1} = μ_{0} \frac{I}{3}$

$B = \frac{μ_{0} I}{6 π R}$

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