Question

A cylindrical conductor of radius $R$ carries a current $i$. The value of magnetic field at a point which is $\frac{R}{4}$ distance inside from the surface is $10T$. The value of magnetic field at point which is $4R$ distance outside from the surface

• A. $\frac{4}{3}T$
• B. $\frac{8}{3}T$
• C. $\frac{40}{3}T$
• D. $\frac{80}{3}T$

Answer 1

Answer: (B)

Magnetic field inside the cylindrical conductor
$B_{in}=\frac{{\mu }_0}{4\pi }\frac{2ir}{R^2}$
$[R=$ radius opf cylinder, $r=$ distance of observation point from axis of cylinder)
Magnetic field outside the cylinder at a distance $r^{\prime }$ from its axis
$B_{\text{out }}=\frac{{\mu }_0}{4\pi }\frac{2i}{r^{\prime }}$
$\Rightarrow \frac{B_{\text{in }}}{B_{\text{out }}}=\frac{r{r}^{\prime }}{R^2}$
$\Rightarrow \frac{10}{B_{\text{out }}}=\frac{\left[R-\frac{R}{4}\right](R+4R)}{R^2}$
$\Rightarrow B_{\text{out }}=\frac{8}{3}T$