An infinitely long hollow conducting cylinder | vedclass

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(D) For an infinitely long hollow cylinder with inner radius $a = R/2$ and outer radius $b = R$ carrying a uniform current density $J$:$1$. For $r < R

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(D) For an infinitely long hollow cylinder with inner radius $a = R/2$ and outer radius $b = R$ carrying a uniform current density $J$:$1$. For $r $2$. For $R/2 \le r \le R$,using Ampere's Law $\oint \vec B \cdot d\vec l = \mu_0 I_{enc}$,we have $B(2\pi r) = \mu_0 J \pi (r^2 - (R/2)^2)$. Thus,$B = \frac{\mu_0 J}{2r} (r^2 - R^2/4) = \frac{\mu_0 J}{2} (r - R^2/4r)$.$3$. For $r > R$,the total current $I = J \pi (R^2 - (R/2)^2) = J \pi (3R^2/4)$ is enclosed. Thus,$B(2\pi r) = \mu_0 I$,which gives $B = \frac{\mu_0 I}{2\pi r}$,meaning $B \propto 1/r$.Comparing this behavior: $B=0$ for $r  R$. Graph $D$ correctly represents this variation.

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field,$|\vec B |$ as a function of the radial distance $r$ from the axis is best represented by:

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