A current i is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius R1 and outer radius R2 . Magnetic field B varies with distance from the axis of the cylinder as

Question

A current i is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius R1 and outer radius R2 . Magnetic field B varies with distance from the axis of the cylinder as (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

Using Ampere's circuital law B = 0 for r≤ R1 B=(μ0 i/2 π(R22-R12))((r2-R12/r)) For R1≤ r≤ R2 and B=(μ 0/2 π )(i/r) textr ≥ textR2 The corresponding B-r graph will be as shown in <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-wdfouv4k6kio.png" />

Q. A current $i$ is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius $R_{1}$ and outer radius $R_{2}$ . Magnetic field $B$ varies with distance from the axis of the cylinder as

Using Ampere's circuital law
$B = 0$ for $r \leq R_{1}$
$B = \frac{μ _{0} i}{2 π ( R _{2}^{2} - R _{1}^{2} )} (\frac{r ^{2} - R _{1}^{2}}{r})$
For $R_{1} \leq r \leq R_{2}$
and $B = \frac{μ _{0}}{2 π} \frac{i}{r}$ $r \geq R_{2}$
The corresponding $B - r$ graph will be as shown in

Q. A current i is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius R1​ and outer radius R2​ . Magnetic field B varies with distance from the axis of the cylinder as

Using Ampere's circuital law B=0 for r≤R1​ B=2π(R22​−R12​)μ0​i​(rr2−R12​​) For R1​≤r≤R2​ and B=2πμ0​​ri​ r≥R2​ The corresponding B−r graph will be as shown in

Q. A current $i$ is uniformly distributed over the cross-section of a long hollow cylindrical wire of inner radius $R_{1}$ and outer radius $R_{2}$ . Magnetic field $B$ varies with distance from the axis of the cylinder as

Using Ampere's circuital law
$B = 0$ for $r \leq R_{1}$
$B = \frac{μ _{0} i}{2 π ( R _{2}^{2} - R _{1}^{2} )} (\frac{r ^{2} - R _{1}^{2}}{r})$
For $R_{1} \leq r \leq R_{2}$
and $B = \frac{μ _{0}}{2 π} \frac{i}{r}$ $r \geq R_{2}$
The corresponding $B - r$ graph will be as shown in