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Essentially the question is to calculate the force exerted by a charged rod perpendicular to an infinite line of charge: $\vec{F}_{\text{rod}\rightarrow \text{line}} =\dots$

My question is it okay to just find $\vec{F}_{\text{line}\rightarrow \text{rod}} =\dots$, basically calculating the force 'the opposite way', since this seems easier to do?

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Newton's 3rd law is fine to use in electrostatics.

Do be aware that in certain situations, the third law is much more subtle; The momentum of the field itself sometimes needs to be taken into account

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