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 $|\overrightarrow{B}|$ as a function of the radial distance $r$ from the axis is best represented by

Question

Dr. Abubacker · Accepted Answer

(d) Case-I $x < \frac{R}{2}$
[image:4_image95.emf]
$\left| \overrightarrow{B} \right| = 0$
Case-II $\frac{R}{2} \leq x < R$
$\int_{}^{}{\overrightarrow{B}.d\overrightarrow{\mathcal{l}} = \mu_{0}l}$
$\left| \overrightarrow{B} \right|2\pi x = \mu_{0}\left\lbrack {\pi x}^{2} - \pi\left( \frac{R}{2} \right)^{2} \right\rbrack J$
$\left| \overrightarrow{B} \right| = \frac{\mu_{0}J}{2x}\left( x^{2} - \frac{R^{2}}{4} \right)$
Case-III $x \geq R$
$\int_{}^{}{\overrightarrow{B}.d\overrightarrow{\mathcal{l}}} = \mu_{0}l$
$\left| \overrightarrow{B} \right|2\pi x = \mu_{0}\left\lbrack \pi R^{2} - \pi\left( \frac{R}{2} \right)^{2} \right\rbrack J$
$\left| \overrightarrow{B} \right| = \frac{\mu_{0}J}{2x}\frac{3}{2}R^{2}$
$\left| \overrightarrow{B} \right| = \frac{3\mu_{0}JR^{2}}{8x}$
So
[image:4_image96.emf]

Q. 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 $|\overrightarrow{B}|$ as a function of the radial distance $r$ from the axis is best represented by

Explanation

Reviewed by Dr. Abubacker

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