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## Homework Statement:

- A grounded conducting sphere of radius R_0 is centered at the origin. If we place a charge +q at z=3R_0, calculate the total induced charge Q on the sphere surface.

## Relevant Equations:

- \sigma = -\epsilon_{zero} dV/dn(R=R_0)

I've come to the result (using cylindrical coordinates)

#\sigma (z) = (-2q) / (pi*sqrt(R_0*(10R_0-6z)^3) )#

and i tried to get #Q# by integrating #2*pi*sqrt(R_0^2-z^2)*\sigma(z)dz# from #-R_0# to #R_0#.

But i can't solve that integral. I tried solving it numerically with arbitrary values and it didn't make sense.

I figured it should be independent of #R_0#, and we should come to# Q=-q/3#...

Any help please? Am i integrating it wrong? Or is it that the charge distribution i got might be wrong?

#\sigma (z) = (-2q) / (pi*sqrt(R_0*(10R_0-6z)^3) )#

and i tried to get #Q# by integrating #2*pi*sqrt(R_0^2-z^2)*\sigma(z)dz# from #-R_0# to #R_0#.

But i can't solve that integral. I tried solving it numerically with arbitrary values and it didn't make sense.

I figured it should be independent of #R_0#, and we should come to# Q=-q/3#...

Any help please? Am i integrating it wrong? Or is it that the charge distribution i got might be wrong?

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