Thursday, March 8, 2018

electrostatics - Electric Field from charged sphere within another charged sphere does not reinforce?


Lets say I have a positively charged conducting sphere of Q. The electric field outside the sphere is



$$E = \frac Q{4\epsilon\pi r^2}.$$


Now suppose this sphere is enclosed inside another hollow conducting sphere of -Q charge. By Gauss law, the electric field is still the same?


Won't the negatively charged outer sphere reinforce the electric field, causing it it be larger?


In another example,


The field from a infinite sheet of charge is


$$ E = \frac \sigma{2\epsilon}. $$


But the field between 2 oppositely charged infinite sheets is


$$ E = \frac \sigma{\epsilon}. $$


Why is this not the case above?




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