Question

A hollow cylindrical wire of radius $R$ carries a current $I$. The magnetic field at any point inside the wire is

• A. zero
• B. $\frac{{\mu }_{0}I}{2\pi R}$
• C. $\frac{{\mu }_{0}I}{2R}$
• D. $\frac{{\mu }_{0}I}{4\pi R}$

Answer 1

Answer: (A)

For a point inside the wire,
Consider an Amperian loop of radius $r(r<R)$
According to Ampere's circuital law
$\oint \vec{B}\cdot \overrightarrow{dl}={\mu }_0{I}_{enclosed}$
$B\left(2\pi r\right)={\mu }_0\left(0\right)\therefore B=0$
For a point outside the wire,
Consider an Amperian loop of radius $r\left(r>R\right)$
According to Ampere's circuital law
$\oint \vec{B}\cdot \overrightarrow{dl}={\mu }_0{I}_{enclosed}$
$B\left(2\pi r\right)={\mu }_{0}I$
$B=\frac{{\mu }_{0}I}{2\pi r}$