Point Charge Repulsion from Spherical Conductor?

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A point charge near a spherical conductor will experience repulsion unless it is within a specific distance from the conductor's surface. The critical distance is calculated as (a/2) * √(e/q), where "a" is the radius of the sphere, "e" is the point charge, and "q" is the charge on the sphere. If the point charge is closer than this distance, it will not be repelled. The discussion seeks assistance in demonstrating this relationship mathematically. Understanding the interaction between point charges and conductors is essential in electrostatics.
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Homework Statement


A point charge e is braught near a spherical conductor of radius "a" having a charge "q".show that the particle will be repelled by the sphere unless its distance from the nearest point of its surface is less than (a/2) *√(e/q) approximately?

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