a question about the total charge on the curved surface

[losheungwai]

for a cylinder of radius 3 and height 5 given by x^2 + y^2 =9 and o<= z <=5
let the electirc charge density be proportional to the distance from the xy - plane.
find the total charge on the curved surfacae of the cylinder.

does it mean find the surface area of the curved surface of the cylinder???

 

[subharpe]

Let the charge density be
ρ = k*r

then the total charge = ∫∫∫ρ*rdrdθdz =k* ∫∫∫r^2drdθdz
where limit of integration on r is 0 to 3, on θ from 0 to 2Π, and on z from 0 to 5.

 

[losheungwai]

but what is k?
does that mean the answer is something k?

Added after 5 minutes:

but isn't this equation for volume of a cone??

 

[subharpe]

Yes, you said the question contains, the charge density is proportional to distance from axis in the x-y plane. Unless you know the proportionality constant, how do you find a numerical answer?

 

[subharpe]

I am sorry, I did not go through the question thoroughly. It is not the right integration i mentioned there. I thought the charge increases radially. But the question contains variation of charge with height, so accordingly the equation has to be changed.