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 $
$B=\frac{\mu_{0}I}{2\pi r}$