COMEDK · Physics · 17. Electrostatics

An electron and a proton having mass \(m_e\) and \(m_p\) respectively, initially at rest, move through the same distance '\(s\)' in a uniform electric field '\(E\)'. If the time taken by them to cover that distance is \(t_e\) and \(t_p\) respectively, then \(t_e / t_p\) is equal to:

A \(\sqrt{\left(\dfrac{m_e}{m_p}\right)}\)
B \(\dfrac{\sqrt{\left(m_e\right)}}{m_p}\)
C \(\sqrt{\left(\dfrac{m_p}{m_e}\right)}\)
D \(\dfrac{m_e}{m_p}\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(\sqrt{\left(\dfrac{m_e}{m_p}\right)}\)

Step-by-step Solution

Detailed explanation

The force experienced by a particle of charge \(q\) in a uniform electric field \(E\) is given by \(F = qE\). Using Newton's second law, the acceleration \(a\) of the particle is \(a = \dfrac{F}{m} = \dfrac{qE}{m}\). For a particle starting from rest, the distance \(s\) covered…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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