Friday, 24 July 2020

electrostatics - Why do charges on the sphere not fly?


Consider a uniformly charged conducting sphere. The $E$ just outside the sphere is $\sigma/\epsilon_0$ and inside the sphere is zero. What about at a point $ON$ the sphere? Here we consider the smallest unit of charge is $dq$ not $e$ (A classical electrostatics case).


What is the electric field experienced by the charge element $dQ$ (the red dot on the sphere)


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I have included five representative charge elements on the sphere and their respective fields on the red dot. By principle of superposition of electric fields one can assume that at the red dot there is a non-zero radial field. So, shouldn't the charge element just fly off?


$E_n$$_e$$_t$ at red dot = E due to charge at yellow dot + E due to charge at blue dot and so on




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