Is this all you have to do for this problem

[charlies1902]

Homework Statement

A nonconducting solid sphere of radius R has a volume charge density that is proportional to the distance from the center. That is rho=Ar for r is less than/equal to , A is a constant. Find the total charge on the sphere.

Homework Equations

The Attempt at a Solution

rho=Ar=Q/V
Q=Ar(4/3)*pi*R^3

Is that it?

 

[SammyS]

No.

Integrate the charge density over the volume of the sphere.

 

[charlies1902]

would've that just be the integral of (Ar dV) which equals Ar*V?

 

[SammyS]

Use dV = 4πr²dr .

Integrate (A)r , with respect to r, from r = 0 to r = R .

 

[charlies1902]

I went in for help on this one and my TA told me that I could do a triple integral for this one or with the integral you provided, but I chose to do the triple integral.

What I did was take the triple integral of Ar*r^2 * sin(theta) in this order: dr,dtheta,dphi
with limits of integration: 0 to R, 0 to pi, 0 to 2pi, respectively
For the answer I got AR^4 * pi

Can you explain how you get the dV = 4πr2dr

 

[SammyS]

The surface area of a sphere of radius r, is 4πr².

So the volume of a spherical shell of thickness dr is given by multiplying the thickness by the surface area.

dV = 4πr² dr.

What's the integral of 4πr² dr, from 0 to R ?