An infinitely long hollow conducting cylinder with inner radius and outer radius carries a uniform current density along its length. The magnitude of the magnetic field, as a function of the radial distance from the axis is best represented by

Question

An infinitely long hollow conducting cylinder with inner radius $\frac{R}{2}$ 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 [2012]

Smart Achievers · Accepted Answer

(4)

For $R$ $B = 0$

For $\frac{R}{2} \leq r < R,$

$B = \frac{μ_{0}}{2} [r - \frac{R^{2}}{2 r}] J$

For $r > R,$ $B = \frac{μ_{0} i}{2 π r}$

i.e., $B \propto \frac{1}{r}$

Hence graph (4) correctly depicts the $| \vec{B} |$ versus $r$ graph.

Solution

Q.
An infinitely long hollow conducting cylinder with inner radius $\frac{R}{2}$ 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 [2012]

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Ans.
(4)

For   $r < \frac{R}{2},$    $B = 0$

For   $\frac{R}{2} \leq r < R,$

$B = \frac{μ_{0}}{2} [r - \frac{R^{2}}{2 r}] J$

For   $r > R,$ $B = \frac{μ_{0} i}{2 π r}$

i.e.,   $B \propto \frac{1}{r}$

Hence graph (4) correctly depicts the $| \vec{B} |$ versus $r$ graph.

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Solution

Q. An infinitely long hollow conducting cylinder with inner radius R2 and outer radius R carries a uniform current density along its length. The magnitude of the magnetic field, |B→| as a function of the radial distance r from the axis is best represented by [2012]

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Ans. (4) For r<R2, B=0 For R2≤r<R, B=μ02[r-R22r]J For r>R, B=μ0i2πr i.e., B∝1r Hence graph (4) correctly depicts the |B→| versus r graph.

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Q.
An infinitely long hollow conducting cylinder with inner radius $\frac{R}{2}$ 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 [2012]

Ans.
(4)

For $r < \frac{R}{2},$ $B = 0$

For $\frac{R}{2} \leq r < R,$

$B = \frac{μ_{0}}{2} [r - \frac{R^{2}}{2 r}] J$

For $r > R,$ $B = \frac{μ_{0} i}{2 π r}$

i.e., $B \propto \frac{1}{r}$

Hence graph (4) correctly depicts the $| \vec{B} |$ versus $r$ graph.