nyungu6f5

2023-03-08

A disc of radius R has surface charge density σ=σ_0r, where r is the distance from the centre of the disc. Find the total charge on the disc.

betssont97

$dA=2\pi rdr\phantom{\rule{0ex}{0ex}}dq=\sigma dA={\sigma }_{0}r\left(2\pi rdr\right)\phantom{\rule{0ex}{0ex}}⇒q=r={\int }_{r=0}^{r=R}{\sigma }_{0}r\left(2\pi rdr\right)\phantom{\rule{0ex}{0ex}}⇒q=2\pi {\sigma }_{0}{\int }_{r=0}^{r=R}{r}^{2}dr\phantom{\rule{0ex}{0ex}}q=2\pi {\sigma }_{0}\left[\frac{{r}^{3}}{3}{\right]}_{r=0}^{r=R}\phantom{\rule{0ex}{0ex}}q=\frac{2\pi {\sigma }_{0}{R}^{3}}{3}$