Question

A cylindrical conductor of radius R carries a current I. The value of the magnetic field at a point which is at R/4 distance inside from the surface is 10 T. Find the value of the magnetic field at a point which is at a 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

The correct option is B $\frac{8}{3}T$

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

Now, magnetic field outside the cylinder at a distance r' from its axis,

$B_{out}=\frac{{\mu }_o}{4\pi }\frac{2i}{r^{\prime }}$

Now, we have

$\frac{B_{in}}{B_{out}}=\frac{r{r}^{\prime }}{R^2}$

$\Rightarrow \frac{10}{B_{out}}=\frac{(R-R/4)(R+4R)}{R^2}$

$\Rightarrow B_{out}=\frac{8}{3}T$