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 $10\, T$. The value of magnetic field at point which is $4 R$ 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
$B_{ in }=\frac{\mu_{0}}{4 \pi} \frac{2 ir }{R^{2}}$
$[R=$ radius opf cylinder, $r=$ distance of observation point from axis of cylinder)
Magnetic field outside the cylinder at a distance $r'$ from its axis
$B_{\text {out }}=\frac{\mu_{0}}{4 \pi} \frac{2 i}{r'}$
$\Rightarrow \frac{B_{\text {in }}}{B_{\text {out }}}=\frac{r r'}{R^{2}}$
$\Rightarrow \frac{10}{B_{\text {out }}}=\frac{\left[R-\frac{R}{4}\right](R+4 R)}{R^{2}}$
$\Rightarrow B_{\text {out }}=\frac{8}{3} T$