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, | overset arrow B| as a function of the radial distance r from the axis, is best represented by:

Question

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, | overset arrow B| as a function of the radial distance r from the axis, is best represented by: (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

r < (R/2) , B=0 r>R , B=(μ 0 I/2 π r) (R/2) < r < R , B=((μ )0 I/2 π r)[(r2 - ((R/2))2/R2 - ((R)2)2)] Solution

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, $∣ ∣ B \to ∣ ∣$ as a function of the radial distance $r$ from the axis, is best represented by:

$r < \frac{R}{2}$ , $B = 0$
$r > R$ , $B = \frac{μ _{0} I}{2 π r}$
$\frac{R}{2} < r < R$ , $B = \frac{( μ ) _{0} I}{2 π r} [\frac{r ^{2} - ( \frac{R}{2} ) ^{2}}{R ^{2} - ( \frac{R}{2} ) ^{2}}]$

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, ∣∣​B→∣∣​ as a function of the radial distance r from the axis, is best represented by:

r<2R​ , B=0 r>R , B=2πrμ0​I​ 2R​<r<R , B=2πr(μ)0​I​[R2−(2R​)2r2−(2R​)2​]

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, $∣ ∣ B \to ∣ ∣$ as a function of the radial distance $r$ from the axis, is best represented by:

$r < \frac{R}{2}$ , $B = 0$
$r > R$ , $B = \frac{μ _{0} I}{2 π r}$
$\frac{R}{2} < r < R$ , $B = \frac{( μ ) _{0} I}{2 π r} [\frac{r ^{2} - ( \frac{R}{2} ) ^{2}}{R ^{2} - ( \frac{R}{2} ) ^{2}}]$