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if the force vector F elect A-->B is in the positive direction form the unit vector r A-->B , the unit vector must be multiplied by a negative number . where does this negative number come from in the Coulomb equation? Does this negative number indicate a repulsive force or an attractive force?
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In general, Coulomb Law is written for two like charges (and the force is repulsive in that case). The beauty of Benjamin Franklin's notation of positive and negative charges is that the same law can be extended for all cases.
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