- #1

Uku

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## Homework Statement

I am given a charge density for a solid sphere

[tex]\rho=14.1\frac{pC}{m^{3}}\frac{r}{R}[/tex]

The r is the distance from the center of the sphere and R is the radius of the whole thing.

[tex]R=5,6cm[/tex]

Now I am asked for the whole charge contained by the sphere.

## Homework Equations

[tex]\rho=\frac{dq}{dV}[/tex]

## The Attempt at a Solution

[tex]dq=\rho dV[/tex]

[tex]dq=4.1\frac{pC}{m^{3}}\frac{r}{R} dV[/tex]

I'll just denote the picocoulomb into B

[tex]q=\frac{B}{R} \int r dV[/tex]

Right, here I land. This is from Halliday, second year thing, I bet they don't expect you to do volume integration in spherical coordinates or anything such. I could write it:

[tex]dV=\frac{4}{3} \pi dr^{3}[/tex]?

Pff...

EDIT:

Ok, now I get it I think:

[tex]q=\frac{B}{R} \int r dV[/tex]

is actually

[tex]q=B \int dV[/tex]

[tex]q=14.1\frac{pC}{m^{3}} \frac{4}{3} \pi r^{3}[/tex]

ought to give me the right answer

EDIT:

It does not.

The right answer is given by

[tex]q=14.1\frac{pC}{m^{3}} \pi r^{3}[/tex]

But how do I land that?

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