- #1
zezima1
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Let's say we have a charge a distance d above the xy plane, which is a grounded conductor. Find the potential at every point. Now this is not a hard problem if you know the method of images. I do however have some questions:
1) The idea is, as reader probably knows, to solve poissons equation by considering a completely different distribution, which obeys the same boundary conditions. The uniqueness theorem guarentees then that this is the right solution.
I just have a little question to this poisson equation thing. As you know the potential must satisfy it because the electric field obeys the maxwell equation
∇ [itex]\bullet[/itex] E = ρ/ε , which in turn comes from Gauss' law. But this is only derivable if we assume that the charge we deal with is a continuos distribution. In that case we can integrate over a volume using the charge density and apply the divergence theorem to obtain the above. In our case however, there is also a point charge, apart from the induced charges on the conductor. Wont that wreak havoc?
2) Solving the problem you find that the total charge induced on the grounded conductor is -q. My book says that this is obvious if you think about it. Unfortunately I fail to see why it is obvious - can someone explain why the induced charge must be -q? :)
1) The idea is, as reader probably knows, to solve poissons equation by considering a completely different distribution, which obeys the same boundary conditions. The uniqueness theorem guarentees then that this is the right solution.
I just have a little question to this poisson equation thing. As you know the potential must satisfy it because the electric field obeys the maxwell equation
∇ [itex]\bullet[/itex] E = ρ/ε , which in turn comes from Gauss' law. But this is only derivable if we assume that the charge we deal with is a continuos distribution. In that case we can integrate over a volume using the charge density and apply the divergence theorem to obtain the above. In our case however, there is also a point charge, apart from the induced charges on the conductor. Wont that wreak havoc?
2) Solving the problem you find that the total charge induced on the grounded conductor is -q. My book says that this is obvious if you think about it. Unfortunately I fail to see why it is obvious - can someone explain why the induced charge must be -q? :)