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I've recently been learning about basic Electricity, and I just started learning about Electric Fields. I came across this problem yesterday, and the solution has been confusing me ever since.

At first glance, my strategy to solve this problem would simply be applying Newton's Second Law to set the Electrostatic Force equal to ma (or F_e = ma). Then, I would substitute qE for F_e and plug in the appropriate values to calculate a.

However, this solution seems to involve using centripetal acceleration to solve the problem, setting F_c = ma_c. This confuses me because I don't see any way that the centripetal force could be involved in this scenario, and also because this solution never seems to actually use the centripetal acceleration; it just keeps a_c as-is.

So, my question is, why is centripetal acceleration involved in the F = ma equation here? Am I missing something to do with the proton in this problem?

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The acceleration can be considered centripetal in the initial moment only. The field causes a perpendicular acceleration, and centripetal accelerations are perpendicular to the path (to the velocity).

While this may be true, though, it is not relevant. The fact that it is centripetal in that moment does not help you in your problem-solving. This is unnecessary information - many things can be true and not useful in which case I would leave them out. Pedagogically I agree it is unnecessarily confusing to indicate a centripetal acceleration in the solution for this task.

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