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Physics
Classical Physics
Electromagnetism
The implications of symmetry + uniqueness in electromagnetism
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[QUOTE="Twigg, post: 6853536, member: 572426"] I don't have the text you are following, but I think I can follow. You have a charge density distribution that is symmetric under a charge-flip + reflection about the xy plane, as you have said. First, you need to consider the intrinsic symmetries of the electric field. Intrinsically, no matter what charge distribution you have, the electric field will flip sign under a charge-flip (since it's proportional to source charge) and the z-component of the E-field will flip sign under reflection about the xy plane (since it is proportional to force and thus acceleration along z). The x and y components of the electric field will be unchanged by the reflection about the xy plane, but they will flip under a charge-flip transformation. Putting all of that together, you find that your electric field must satisfy: $$ E_x(-z) = -E_x(z)$$ $$E_y(-z) = -E_y(z)$$ $$E_z(-z) = E_z(z)$$ This field has the dipole characteristic that you were looking for. [/QUOTE]
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Physics
Classical Physics
Electromagnetism
The implications of symmetry + uniqueness in electromagnetism
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