Two identical small conducting spheres, each of radius R, are far apart compared with R. Initially they carry charges Q and 0. They are connected by a thin wire and then disconnected. The decrease in electrostatic energy is approximately:
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Question

Two identical small conducting spheres, each of radius R, are far apart compared with R. Initially they carry charges Q and 0. They are connected by a thin wire and then disconnected. The decrease in electrostatic energy is approximately:

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G1 Physics · Accepted Answer

Initially Uᵢ=Q²/(8πε₀R). After connection, identical spheres share charge equally, Q/2 each. Final energy U f = 2 [ ( Q / 2 ) 2 / ( 8 π ε 0 R ) ] = Q 2 / ( 16 π ε 0 R ) . U_f=2[(Q/2)²/(8πε₀R)]=Q²/(16πε₀R). U f ​ = 2 [( Q /2 ) 2 / ( 8 π ε 0 ​ R )] = Q 2 / ( 16 π ε 0 ​ R ) . Thus decrease Uᵢ- U f = Q 2 / ( 16 π ε 0 R ) . U_f=Q²/(16πε₀R). U f ​ = Q 2 / ( 16 π ε 0 ​ R ) .