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

We need to find the magnetic field $$B$$ as a function of radial distance $$r$$ from the axis of an infinitely long hollow conducting cylinder of radius $$R$$ that carries a uniform current along its surface.

We apply Ampere's Law: $$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}$$.

For $$r < R$$: Choose a circular Amperian loop of radius $$r < R$$ centred on the axis. Since the current flows only on the surface at $$r = R$$, this loop encloses zero current. By Ampere's Law: $$B(2\pi r) = 0$$, so $$B = 0$$ for all $$r < R$$.

For $$r > R$$: Choose a circular Amperian loop of radius $$r > R$$. This loop encloses the entire surface current $$I$$. By Ampere's Law: $$B(2\pi r) = \mu_0 I$$, giving $$B = \dfrac{\mu_0 I}{2\pi r}$$, which decreases as $$\dfrac{1}{r}$$.

The correct graph shows $$B = 0$$ for $$r < R$$ and $$B \propto \dfrac{1}{r}$$ for $$r > R$$.

The answer is Option D.