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Do I have to re-define electric field strength in Centre of Mass frame

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So lets say I'm computing the torque as a result of the interaction between two electric dipoles in the lab frame. Lets imagine they are in some electric field.

I then do : τ = r×F

If I now switch to the centre of mass frame I have to find their position vectors from the COM.

Why do I not have to re-define the electric field strength vector and ultimately the force vector on each dipole with respect to the centre of mass frame ?

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