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Question

An electron having charge e and mass m at rest starts from the lower plate of two metallic plates separated by a distance d. If the potential difference between the plates is V, the time taken by the electron to reach the upper plate is

A
2md2eV
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B
md2eV
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C
md22eV
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D
4md2eV
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Solution

The correct option is A √2md2eVElectric field between the plates is towards lower plate of magnitude, E=Vd Force experience by the electron due to electric field E is towards upper plate of magnitude, F=eE=eVd From Newton's second law of motion, the acceleration of the electron, a=Fm=eVmd From equation of motion, d=ut+12at2 Since the initial velocity of electron is zero.i.e. u=0 and the time taken by electron to reach upper plate is t, so, d=12at2 ⇒t=√2da Substituting the value of a in the above equation, we get t=√2dmdeV ∴t=√2md2eV Hence, option (A) is the correct answer.

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