Mathematics, 04.04.2020 11:03 ayandjay01
Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y2 (measured in coulombs per square meter). Find the total charge on the disk.
Answers: 2
coulombs per square meter. 
so that the charge density at (x,y) is,
so that,
where A is the surface of disk.
![=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta](/tpl/images/0582/2178/f6c15.png)
![=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi](/tpl/images/0582/2178/3af50.png)
![=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi](/tpl/images/0582/2178/b58be.png)
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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rh...
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