A cylindrical conductor of radius $'R'$ carries a current $'i'$. The value of magnetic field at a point which is $R/4$ distance inside from the surface is $10\,T$. Find the value of magnetic field at point which is $4R$ distance outside from the surface
Diffcult
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Magnetic field inside the cylindrical conductor
$\mathrm{B}_{\mathrm{in}}=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{ir}}{\mathrm{R}^{2}} \quad(\mathrm{R}=$ Radius of cylinder $\mathrm{r}=$ distance of observation point from axis of cylinder)
or $\mathrm{r}=\mathrm{R}-\frac{\mathrm{R}}{4}$
Magnetic field out side the cylinder at a distance $\mathrm{r}^{\prime}$ from it's axis $\mathrm{B}_{\text {out }}=\frac{\mu_{0}}{4 \pi} \cdot \frac{2 \mathrm{i}}{\mathrm{r}^{\prime}}$
$\Rightarrow \frac{B_{\text {in }}}{B_{\text {out }}}=\frac{rr^{\prime}}{R^{2}} \Rightarrow \frac{10}{B_{\text {out }}}=\frac{\left(R-\frac{R}{4}\right)(R+4 R)}{R^{2}}$
$\Rightarrow \frac{10}{\mathrm{B}_{\mathrm{out}}}=\frac{\frac{3}{4} \mathrm{R} \times 5 \mathrm{R}}{\mathrm{R}^{2}} \Rightarrow \mathrm{B}_{\mathrm{out}}=\frac{8}{3}\, \mathrm{T}$
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