Question
An infinitely long hollow conducting cylinder with inner radius $$\frac{R}{2}$$ and outer radius $$R$$ carries a uniform current density along its length. The magnitude of the magnetic field, $$\left| {\vec B} \right|$$ as a function of the radial distance $$r$$ from the axis is best represented by
A.
B.
C.
D.
Answer :
Solution :
$$\eqalign{ & {\text{For}}\,r < \frac{R}{2},\,\,\,\,B = 0 \cr & {\text{For}}\,\frac{R}{2} \leqslant r < R \cr & B = \frac{{{\mu _0}}}{2}\left[ {r - \frac{{{R^2}}}{{2r}}} \right]J \cr & {\text{For}}\,r > R,\,\,\,B = \frac{{{\mu _0}i}}{{2\pi r}} \cr} $$
$$\eqalign{ & {\text{For}}\,r < \frac{R}{2},\,\,\,\,B = 0 \cr & {\text{For}}\,\frac{R}{2} \leqslant r < R \cr & B = \frac{{{\mu _0}}}{2}\left[ {r - \frac{{{R^2}}}{{2r}}} \right]J \cr & {\text{For}}\,r > R,\,\,\,B = \frac{{{\mu _0}i}}{{2\pi r}} \cr} $$