Question

Electric charge is distributed over the disk
x^2 + y^2 ≤ 11 so that the charge density at (x,y) is σ(x,y) = 19 + x^2 + y^2 coulombs per square meter.
Find the total charge on the disk.
?????

Answer 1

the disk is radius\[r=\sqrt11\]converting to polar coordinates\[x=r \cos \theta\]\[y=r \sin \theta\]making these substitutions gives\[\sigma (x,y)=19+11(\cos^2 \theta +\sin^2 \theta)=21\]in polar coordinates\[dA=rdrd \theta\]so our integral is now\[\int\limits_{0}^{2 \pi}\int\limits_{0}^{\sqrt11}21rdrd \theta=\int\limits_{0}^{2 \pi}21{(\sqrt11)^2\over2}d \theta=\int\limits_{0}^{2 \pi}{231\over2}d \theta=231 \pi\]

Answer 2

so 341pi !?

Answer 3

Yet another slight typo...
19+11=30
put 30 where I have 21 and it will be correct
sorry again...

Answer 4

i meant 330 !

Answer 5

yeah but i plug it in and its not correct !

Answer 6

really? hmm.. let me see

Answer 7

ok

Answer 8

I guess you have to keep r as a variable since you integrate across it, so\[σ(x,y)=19+r^2(\cos^2θ+\sin^2θ)=19+r^2\]\[\int\limits_{0}^{2\pi}\int\limits_{0}^{\sqrt11}19r+r^3drd \theta={539\pi \over2}\]
Please let me know if this is right.

Answer 9

finally!

Answer 10

awesome thanks ! it makes sense too !

Answer 11

my bad earlier, I apologize.

Answer 12

haha no man thank u for helping me out ! its math we all do mistakes !