GATE EC 2016 Set 2 — Question 65
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Electromagnetics → Maxwell's Equations
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Question
A positive charge is placed at between two infinite metal plates placed at and at respectively. The metal plates lie in the plane.
The charge is at rest at , when a voltage is applied to the plate at and voltage is applied to the plate at . Assume that the quantity of the charge is small enough that it does not perturb the field set up by the metal plates. The time that the charge takes to reach the right plate is proportional to
Correct answer
(C) d / √(V)
Solution
1.Identify the potential difference and electric field:
The potential at is and at is .The potential difference between the plates is .
The distance between the plates is .
The electric field between the plates is uniform and is given by:
2.Determine the force and acceleration on the charge:
The force on the charge is:The acceleration of the charge (mass ) is:
3.Calculate the time to reach the right plate:
The charge starts from rest () at and needs to reach . The distance to travel is .Using the equation of motion :
4.Conclusion:
The time is proportional to .This matches option (C).
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