Calculate the force on charge at centre

[gandharva_23]

A charge Q is placed at the center of a spherical shell of radius R . Another charge Q is kept at a distance 2R from the centre of the shell . What will be the force exerted by shell on the charge placed at the centre of the shell ?

I know that the total force on the charge at centre will be force due to shell on on charge at centre (assuming the other charge was not there ) + the force charge at centre due to charge placed at 2R assuming the sphere was not there .(principal of superposition) . hence i can say that the total force on the charge at centre will be (K*q*q)/(2R)^2 . but i cannot understand how to calculate the force on charge at centre due to the shell alone when the other charge at 2R is also present . please help ...

 

[Andrew Mason]

A charge Q is placed at the center of a spherical shell of radius R . Another charge Q is kept at a distance 2R from the centre of the shell . What will be the force exerted by shell on the charge placed at the centre of the shell ?

I know that the total force on the charge at centre will be force due to shell on on charge at centre (assuming the other charge was not there ) + the force charge at centre due to charge placed at 2R assuming the sphere was not there .(principal of superposition) . hence i can say that the total force on the charge at centre will be (K*q*q)/(2R)^2 . but i cannot understand how to calculate the force on charge at centre due to the shell alone when the other charge at 2R is also present . please help ...

Assuming it is a conducting, uncharged shell, the charges will move around until they are all at equal potential. This means that the charges on the inside and outside surface will distribute so that there is always 0 field in the middle. Using Gauss' law, for each element of area of the shell, one can see that the net flux is 0. So I don't see how there would be a force by the shell on either charge.

AM