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

Magnetic field inside the cylindrical conductor
 

$B_{in}=\frac{{\mu }_0}{4\pi }\cdot \frac{2ir}{R^2}$

(R = Radius of cylinder, r = distance of observation point from axis of cylinder)
Magnetic field outside the cylinder at a distance $r\text{'}$ from it’s axis  

 $\begin{array}{c}{B}_{\text{out }}=\frac{{\mu }_0}{4\pi }\cdot \frac{2i}{r^{\mathrm{\prime }}}\\ \Rightarrow \frac{B_{\text{in }}}{B_{\text{out }}}=\frac{r{r}^{\mathrm{\prime }}}{R^2}\Rightarrow \frac{10}{B_{\text{out }}}=\frac{\left(R-\frac{R}{4}\right)(R+4R)}{R^2}\Rightarrow B_{\text{out }}=\frac{8}{3}T\end{array}$