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(D) For a cylindrical conductor with inner radius $a = R$ and outer radius $b = 2R$,the magnetic field $B$ at a distance $r$ from the center (where $a

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$\frac{5{\mu _0}i}{36\pi R}$

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(D) For a cylindrical conductor with inner radius $a = R$ and outer radius $b = 2R$,the magnetic field $B$ at a distance $r$ from the center (where $a $B(2\pi r) = \mu_0 I_{enclosed}$$I_{enclosed} = i \left( \frac{r^2 - a^2}{b^2 - a^2} \right)$Substituting $a = R$,$b = 2R$,and $r = \frac{3R}{2}$:$I_{enclosed} = i \left( \frac{(\frac{3R}{2})^2 - R^2}{(2R)^2 - R^2} \right) = i \left( \frac{\frac{9R^2}{4} - R^2}{4R^2 - R^2} \right) = i \left( \frac{\frac{5R^2}{4}}{3R^2} \right) = i \left( \frac{5}{12} \right)$Now,$B = \frac{\mu_0 I_{enclosed}}{2\pi r} = \frac{\mu_0 (i \cdot \frac{5}{12})}{2\pi (\frac{3R}{2})}$$B = \frac{5\mu_0 i}{12 \cdot 2\pi \cdot \frac{3R}{2}} = \frac{5\mu_0 i}{36\pi R}$

What is the magnetic field at point $P$ located at a distance of $\frac{3R}{2}$ from the center of the cylindrical conductor with inner radius $R$ and outer radius $2R$ carrying a current $i$?

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