A thick uniformly charged hollow cylinder of inner radius $a$ and outer radius $b$ rotates with constant angular speed $\omega $ about its axis $APB$, charge density$ = \rho $
Given that $L >>> a$ $L >>> b$ and $P$ is mid point of $AB$. Choose the incorrect option
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Consider a eylinder of radius $r$ and thickness $\mathrm{dr}.$
Charge on cylinder $\mathrm{d} \mathrm{Q}=\rho .2 \pi \mathrm{r} \mathrm{dr} \mathrm{L}$
${\rm{dI}} = \frac{{{\rm{d}}\theta \omega }}{{2\pi }}$
$\mathrm{d} \beta=\mu_{0} \mathrm{nI}=\mu_{0} \frac{1}{\mathrm{L}} \frac{\mathrm{d} \theta \omega}{2 \pi}$
$\mathrm{dB}=\int \frac{\mu_{0} \omega}{2 \pi \mathrm{L}} \rho .2 \pi \mathrm{r} \mathrm{dr} \mathrm{L}=\mu_{0} \omega \rho \int_{a}^{b} r \mathrm{dr}$
$=\frac{\mu_{0} \omega \rho \cdot\left(\mathrm{b}^{2}-\mathrm{a}^{2}\right)}{2}$
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