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

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The discussion revolves around calculating the time it takes for an electron, positioned at an angle of 45° inside a cavity of a solid dielectric sphere, to reach the sphere's edge. The electric field within the cavity is determined to be ρa/3, directed towards the sphere's center. The challenge arises from the variable electric field once the electron enters the sphere. Participants express uncertainty about whether to calculate the time until the electron hits point P or to consider its subsequent motion into the sphere. Clarification and assistance are requested to resolve the problem.
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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
 
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