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1. Homework Statement
An infinite conducting sheet has a hemispherical bubble of radius a. (Refer to the diagram)
2. The attempt at a solution
ok i know the boundary conditions should be (Phi refresents the potential)
And we are working in CGS units... units with which i am not entire comfortable.
Z is the vertical and Y is the horizontal
[itex] \Phi(y, \sqrt{a^2  y^2}) = 0 [/itex] for [itex] a\leq y\leq a [/itex]
[itex] \Phi(y,0) = 0 [/itex] where y<= a and y=> a
Should i be considering the 3D case because it does say bubble...
i know how to do this for a plane and a sphere but this 'mixed' case has got me confused.
i thought of locating a charge at a point (z0+2a,0) and that satisifes condition 1 but not condition 2
it doesnt work for any point other tan this one so no..
maybe i am not thinking about something and so im stuck!
i think that there would be more than one point charge on th segment y = z0 +2a
Thanks for your input!
An infinite conducting sheet has a hemispherical bubble of radius a. (Refer to the diagram)
2. The attempt at a solution
ok i know the boundary conditions should be (Phi refresents the potential)
And we are working in CGS units... units with which i am not entire comfortable.
Z is the vertical and Y is the horizontal
[itex] \Phi(y, \sqrt{a^2  y^2}) = 0 [/itex] for [itex] a\leq y\leq a [/itex]
[itex] \Phi(y,0) = 0 [/itex] where y<= a and y=> a
Should i be considering the 3D case because it does say bubble...
i know how to do this for a plane and a sphere but this 'mixed' case has got me confused.
i thought of locating a charge at a point (z0+2a,0) and that satisifes condition 1 but not condition 2
it doesnt work for any point other tan this one so no..
maybe i am not thinking about something and so im stuck!
i think that there would be more than one point charge on th segment y = z0 +2a
Thanks for your input!
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