The system has totally Q charges. 1. What is the P.E. of the system when all the

Question

  The system has totally Q charges. 1. What is the P.E. of the system when all the charges are puton one sphere? 2. All the charges are put on one sphere. Then we connect thetwo spheres using a metal wire. Does the electrostatics energyconserve ? It seems that work done on the charges to travel fromhigher potential to lower before equilibrium. How about the total energy, conserves or not? If my thought isright, the total energy is conserved. Please help to explain the problem.   The system has totally Q charges. 1. What is the P.E. of the system when all the charges are puton one sphere? 2. All the charges are put on one sphere. Then we connect thetwo spheres using a metal wire. Does the electrostatics energyconserve ? It seems that work done on the charges to travel fromhigher potential to lower before equilibrium. How about the total energy, conserves or not? If my thought isright, the total energy is conserved. Please help to explain the problem.

Explanation / Answer

1.When the system consists of more than two chargedparticles,we can obtain the total potential energy of the system bycalculating U for every pair of charges and summing the termsalgebraically.For example,the total potential energy of the systemof three charges is U = ke* (q1q2/r12+ q1q3/r13 +q2q3/r23) when the system has totally Q charges then U = ke* (Q * Q/r) = ke*(Q2/r) ke= (1/4o) = 9 *109 Nm2/C2 and r is the distancebetween the two charges. 2.When the two spheres are connected using a metal wire thenthe charge is equally distributed on both the spheres.Hence theelectrostatics energy is conserved.The charges travel from thehigher to the lower potential before equilibrium is reached.Thetotal energy is conserved.

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