2
$\begingroup$

Electric charge is distributed over the disk $x^2 + y^2 \leq 5$ so that the charge density at $(x,y$) is $\sigma(x,y) = 2 + x^2 + y^2$ coulombs per square meter. Find the total charge on the disk.

$$\int_0^{2\pi}\int_0^5(2+r^2)\space r\space dr\space d\theta=\frac{725\pi}2$$

is not the right answer. I don't know why. Any help?

enter image description here

$\endgroup$
2
  • $\begingroup$ I am being marked wrong when I input my answer online. $\endgroup$
    – user5826
    Commented May 1, 2014 at 2:56
  • 2
    $\begingroup$ The radius is $\sqrt{5}$, not $5$. You have the wrong limit of integration. $\endgroup$
    – IAmNoOne
    Commented May 1, 2014 at 2:57

1 Answer 1

4
$\begingroup$

The radius of the disk is $\sqrt{5}$, not $5$. Change your upper integration limit and you'll get the right answer. (The formula is $x^2+y^2=r^2$, not $\dots = r$.)

$\endgroup$
1
  • $\begingroup$ $=\frac{45\pi}2$...Thanks $\endgroup$
    – user5826
    Commented May 1, 2014 at 3:01

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .