Question 60 of 276

An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface.
Choose the correct representation of magnetic field $\left(B\right)$as a function of radial distance $\left(r\right)$ from the axis of cylinder.

ABCD

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Answer: (D)

According to Ampere's law,
$\oint \vec{B}\cdot d\vec{l}={\mu }_{0}i$
Inside the hollow cylinder, current will be zero. Therefore, magnetic field will also be zero.
Outside the cylinder,
$B2\pi r={\mu }_{0}i \Rightarrow B=\dfrac{{\mu }_{0}i}{2\pi r}\Rightarrow B\propto \dfrac{1}{r}$
Hence, the correct answer is D.