91Ó°ÊÓ

We have given,

inner conductor of radius =${\mathrm{R}}_1$

outer conductor of radius =${\mathrm{R}}_2$

Current =$\mathrm{I}$

we have to find three magnetic fields within the inner conductor, in the space between the conductors, and outside the outer conductor.

Using ampere's law for closed loop

$$\begin{gathered} {∫}_0^{\mathrm{L}}\stackrel{→}{B}\stackrel{→}{dl}={\mathrm{μ}}_0{I}_{enclosed} \\ Then, \\ B{\left[L\right]}_0^{2\mathrm{π}r}={\mathrm{μ}}_0{I}_{enclosed} \\ B.2\mathrm{π}r={\mathrm{μ}}_0{I}_{enclosed} \\ B=\frac{{\mathrm{μ}}_0{I}_{enclosed}}{2\mathrm{π}r}.................................\left(1\right) \end{gathered}$$

The current density inside the radius${\mathrm{R}}_1$is given as

localid="1649504415272" ${\mathrm{J}}_1=\frac{\mathrm{i}}{\mathrm{A}}=\frac{\mathrm{i}}{{\mathrm{Ï€¸é}}_1^2}$

The current density for radial path will be

localid="1649504486700" ${\mathrm{J}}_{\mathrm{r}}=\frac{\mathrm{i}}{\mathrm{A}}=\frac{{\mathrm{i}}_{\mathrm{enclosed}}}{{\mathrm{Ï€°ù}}^2}$

Then enclosed current will be

localid="1649504528820" $$\begin{gathered} {\mathrm{J}}_1={\mathrm{J}}_{\mathrm{r}} \\ \frac{\mathrm{i}}{{\mathrm{Ï€¸é}}_1^2}=\frac{{\mathrm{I}}_{\mathrm{enclosed}}}{{\mathrm{Ï€°ù}}^2} \\ {\mathrm{I}}_{\mathrm{enclosed}}=\frac{{\mathrm{r}}^2}{{\mathrm{R}}_1^2}×\mathrm{I} \end{gathered}$$

Put this value in equation (1)

$\mathrm{B}=\frac{{\mathrm{μ}}_0\mathrm{Ir}}{2{\mathrm{Ï€¸é}}_1^2}$

For the magnet field between the two conductor.

Simply it will be arbitrary

$$\begin{gathered} {∫}_0^{\mathrm{L}}\stackrel{→}{B}\stackrel{→}{dl}={\mathrm{μ}}_{0}I \\ Then, \\ B{\left[L\right]}_0^{2\mathrm{π}r}={\mathrm{μ}}_{0}I \\ B.2\mathrm{π}r={\mathrm{μ}}_{0}i \\ B=\frac{{\mathrm{μ}}_{0}I}{2\mathrm{π}r} \end{gathered}$$

For the a magnetic field outside the current carrying conductor will be zero. since there is not have any current enclosed.

$\mathrm{B}=0.$

We have given,

inner conductor of radius =${\mathrm{R}}_1$

outer conductor of radius =${\mathrm{R}}_2$

Current =$\mathrm{I}$

we have to find three magnetic fields within the inner conductor, in the space between the conductors, and outside the outer conductor graphs.

The graph between the three region magnetic field is varying like as shown in the figure below.