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

Beginner2023-03-09Added 3 answers

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