How Long Will It Take for an Electron to Reach the Sphere's Edge?

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SUMMARY

The discussion centers on calculating the time it takes for an electron to reach the edge of a solid dielectric sphere from a cavity within it. The electric field inside the cavity is determined to be ρa/3, directed parallel to the line connecting the centers of the sphere and the cavity. The electron starts at an angle of θ = 45° and must first reach point P before entering the sphere, where the electric field becomes variable. Participants express uncertainty about the approach to solve the problem, particularly regarding whether to calculate the time to point P or the sphere's edge.

PREREQUISITES
  • Understanding of electrostatics, specifically electric fields in dielectric materials.
  • Familiarity with the concepts of volume charge density (ρ) and its implications.
  • Knowledge of kinematics, particularly motion under variable electric fields.
  • Basic calculus for solving integrals related to electric field equations.
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  • Study the behavior of electric fields in dielectric materials, focusing on solid dielectrics.
  • Learn how to calculate the motion of charged particles in electric fields, including variable fields.
  • Explore the concept of electric potential and its relationship to electric fields in cavities.
  • Investigate the principles of kinematic equations applied to charged particle motion in electrostatic fields.
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Tanya Sharma
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Homework Statement



A cavity of radius r is present inside a solid dielectric sphere of radius R, having a volume charge density of ρ. The distance between the centers of the sphere and the cavity is a. An electron e is kept inside the cavity at an angle θ = 45° as shown. How long will it take to touch the sphere again?


Homework Equations





The Attempt at a Solution



The electric field inside the cavity is ρa/3 directed parallel to the line joining the centers of the sphere and the cavity ,i.e parallel to OC .

The electron is at E .So it should reach point P .After that it will enter the sphere .But the electric field will be variable inside the sphere .I am unable to proceed from here.

Not sure whether my approach is correct .

I would be grateful if somebody could help me with the problem.
 

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You sure they don't just want you to calculate when it hits P ?
 
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You are right .

Thank you very much
 
Last edited:

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