What Condition Must q2 Meet to Experience a Repelling Force?

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SUMMARY

The discussion focuses on determining the condition under which the charge q2 experiences a repelling force when placed near a grounded sphere and another charge q1. The sphere has a radius 'a' and is positioned between q1 and q2, with distances of 2a and 4a from the center O of the sphere, respectively. To analyze the forces, the use of image charges is essential, where the sphere is replaced by two image point charges within its interior. The electrical force on charge q2 can be calculated using the formula F=qE, where E is the electric field generated by the other charges.

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Reshma
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A grounded sphere of radius 'a' is placed between point charges q1 and q2 with its centre O lying on the straight line joining q1 and q2. The distances of q1 and q2 from O are 2a and 4a respectively. Find the condition that the charge q2 experiences a repelling force.

My question:
How do I formulate the electrical force? I tried calculating the force for individual charges taking into account their image charges. But that makes my solution very cumbersome and I don't seem to be arriving at any particular answer. Help needed.
 
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Electric force on a charge q is just F=qE. You are right about using image charges - you replace the sphere with two 'image' point charges in its interior. You'll need to find what these charges are, and were they're located. Then you just add the forces due to each of three of the charges on the fourth one.

Your approach is entirely correct, you just need to finish the algebra.
 

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