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Homework Statement
There is a uniform electric field with strength [itex] E_0 [/itex].Then we place a conducting spherical shell with a dipole at the center of it,inside the field,somehow that the dipole moment is prependicular to the initial field.Find the potential/electric field of the new configuration.(It should be solved in spherical coordinates [itex] (r,\theta,\phi) [/itex] and the answer is independent of [itex] \phi [/itex].)
Homework Equations
[itex] \phi(r,\theta)=\Sigma _{l=0} ^∞ (A_l r^l+\frac{B_l}{r^{l+1}})P_l(cos \theta) [/itex]
Where [itex] A_l [/itex] and [itex] B_l [/itex] are constants to be determined and [itex] P_l(x) [/itex] are the legendre polynomials.
I'm not sure,but maybe it can be solved by the method of image charges too.
The Attempt at a Solution
I tried to use the formula above but I got so confused about the boundary conditions and also how to use them to calculate As and Bs.