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darwin59
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Homework Statement
A point charge +q is situated a distance a from the center of a grounded conducting sphere of radius R. Find the induced surface charge on the sphere as a function of θ. Integrate this to get the total induced charge.
Homework Equations
σ=-εo*∂V/∂r
Q=∫σ da
The Attempt at a Solution
I've already figured out σ to be (-q/4∏)(a2/R-R)(R2+a2-2aRcosθ)-3/2. I also know that Q needs to equal -q. But I'm having trouble completing the integral to get to just -q. The way I've tried it is ∫[itex]^{2∏}_{0}[/itex]∫[itex]^{∏}_{0}[/itex] σ R2sinθ dθd[itex]\Phi[/itex]; but I'm not getting it to reduce to just -q. I'm confident in my answer for σ, so my problem must be in my integral, but I can't figure out what it is.
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