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First time poster here! EDIT: SOLVED!!

Thanks, I figured out from the related links at the bottom of the page. >_>b

Find the electric field inside a sphere which carries a charge density proportional

to the distance from the origin, [tex]\rho[/tex] = kr, for some constant k.

[tex]\oint E.da[/tex]

[tex]a = 4 \pi r^2/3[/tex]

[tex]da = 4 \pi r^2[/tex]

[tex]\rho = kr[/tex]

[tex]E = q/(r^2 4 \pi \epsilon _0)[/tex]

Where q = charge inside

[tex]\oint E \bullet da = \int q/(r^2 4 \pi \epsilon _0) \bullet 4 \pi r^2[/tex]

The 4 pi r^2 terms cancel, leaving on the right

[tex]q/ \epsilon_0[/tex]

Substitute rho into the eqn. as to integrate all dimensions of the sphere

[tex] \int \rho d \tau / \epsilon_0[/tex]

Here's where I get stuck, I know that

[tex] \rho = kr [/tex]

What do I do with [tex]d \tau[/tex]? I'd imagine that it'd be easiest to do in spherical coordinates, so do I just add dr, dtheta, drho?

Also... How do I put a dot into this LaTex thing?

Thank you!

Thanks, I figured out from the related links at the bottom of the page. >_>b

## Homework Statement

Find the electric field inside a sphere which carries a charge density proportional

to the distance from the origin, [tex]\rho[/tex] = kr, for some constant k.

## Homework Equations

[tex]\oint E.da[/tex]

[tex]a = 4 \pi r^2/3[/tex]

[tex]da = 4 \pi r^2[/tex]

[tex]\rho = kr[/tex]

[tex]E = q/(r^2 4 \pi \epsilon _0)[/tex]

Where q = charge inside

## The Attempt at a Solution

[tex]\oint E \bullet da = \int q/(r^2 4 \pi \epsilon _0) \bullet 4 \pi r^2[/tex]

The 4 pi r^2 terms cancel, leaving on the right

[tex]q/ \epsilon_0[/tex]

Substitute rho into the eqn. as to integrate all dimensions of the sphere

[tex] \int \rho d \tau / \epsilon_0[/tex]

Here's where I get stuck, I know that

[tex] \rho = kr [/tex]

What do I do with [tex]d \tau[/tex]? I'd imagine that it'd be easiest to do in spherical coordinates, so do I just add dr, dtheta, drho?

Also... How do I put a dot into this LaTex thing?

Thank you!

Last edited: