Answer:
[tex]B = \frac{\mu_0 \rho r^2 \omega}{2}[/tex]
Explanation:
Let the position of the point where magnetic field is to be determined is at distance "r" from the axis of cylinder
so here total charge lying in this region is
[tex]q = \rho(\pi r^2 L)[/tex]
now magnetic field inside the cylinder is given as
[tex]B = \frac{\mu_0 N i}{L}[/tex]
here current is given as
[tex]i = \frac{q\omega}{2\pi}[/tex]
[tex]i = \frac{\rho (\pi r^2 L) \omega}{2\pi}[/tex]
[tex]i = \frac{\rho r^2 L \omega}{2}[/tex]
now magnetic field is given as
[tex]B = \frac{\mu_0 \rho r^2 L \omega}{2L}[/tex]
[tex]B = \frac{\mu_0 \rho r^2 \omega}{2}[/tex]
