A charged non-conducting thin Disc of radius R is spinning with an angular speed $\text{'}\omega \text{'}$ . Surface charge density of disc is $\text{'}\sigma \text{'}$ then magnetic field at its centre is.

$\text{d}I=2\pi y\text{d}y\sigma \frac{\omega }{2\pi }$

$\text{d}I=\sigma \omega .y\text{d}y$

$\text{dB}=\frac{{\mu }_0}{2}\frac{\text{d}I{y}^2}{{\left(y^2+x^2\right)}^{3/2}}$

$\text{B}=\frac{{\mu }_0\sigma \omega y^3\text{d}y}{2{\left(y^2+x^2\right)}^{3/2}}$

$\text{B}={\displaystyle {\int }_{\text{O}}^{\text{R}}\frac{{\mu }_0\sigma \omega y^3\text{d}y}{2{\left(y^2+x^2\right)}^{3/2}}}$

$=\frac{{\mu }_0\sigma \omega }{2}{\displaystyle {\int }_{\text{O}}^{\text{R}}\frac{y^3\text{d}y}{{\left(y^2+x^2\right)}^{3/2}}}$

${\text{B}}_{\text{curture}}=\frac{{\mu }_0\sigma \omega }{2}{\displaystyle {\int }_{\text{O}}^{\text{R}}\frac{y^3\text{d}y}{y^3}}$

${\text{B}}_{\text{curture}}=\frac{{\mu }_0\sigma \omega \text{R}}{2}$