GATE EC 2017 Set 2 — Question 53
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Electromagnetics → Maxwell's Equations
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Question
An electron () is moving in free space with velocity m/s towards a stationary electron () far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is __________ m.[Given, mass of electron kg, charge of electron C, and permittivity F/m]
Correct answer
4.55 to 5.55
Solution
To find the distance of closest approach, we use the principle of conservation of energy.
1.Initial State (Far away):
The moving electron () has kinetic energy, and the potential energy is zero because they are far apart.2.Final State (Closest approach):
At the point of closest approach, the moving electron comes to a momentary rest relative to the stationary electron. Assuming the stationary electron () is fixed in position, the kinetic energy is zero, and the energy is entirely electrostatic potential energy.3.Conservation of Energy:
Solving for :4.Substitution of Values:
Given:- C
- kg
- m/s
- F/m
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