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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

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Solution

The correct option is **A** √2md2eV

Electric 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.

Electric 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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