# How to compute electrical charge over semi circumference with linear density $\rho_l = k\sin\phi$ without using calculus

The semi circumference has a radio R is electrified with linear density $\rho_l = k \sin \phi$ ($k$ = constant). Determine its total charge.

Answer: $2kR$

Given: $dQ = \rho_l\cdot R \cdot d\phi$
$Q = \int_{0}^{\pi}R\cdot k\cdot \sin\phi \,d\phi\Rightarrow Q = R.k\cdot\underbrace{(-cos(\phi)|_{0}^{\pi})}_{=2} = 2kR$