Find the Speed of a Charge Placed on a Square's Center

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To find the speed of a charge placed at the center of a square with different charges at the corners, the total energy of the system must be calculated as the sum of the work done to bring each charge to the square. The kinetic energy equation, U = mv²/2, can then be used to determine the velocity of the central charge. The charges at the corners are Q, 2Q, -3Q, and 6Q, and since they are fixed, the potential energy U of the central charge Q needs to be evaluated. The symmetry of the charge distribution affects the movement of the central charge, but in this case, the charges are not symmetric. Understanding the potential energy interactions is crucial for solving the problem accurately.
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Hi, I have a question about a problem. Four different charges are placed on the corners of a square, and then a fifth one is placed on the center. I need to find the speed this fifth charge would have at a great distance.

The total energy of the system should be the sum of the work to bring each charge to the square right? So, the total work equals U, and the velocity of the charge can be found from U=Ek, U=mv^2/2. It seems right to me, but I just can't get the right answer. I appreciate the help, thanks.
 
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anyone??

can anyone please help me??
thanks..
 
Are all the charges the same? It depends on the system. If the system is symmetric in any kind of way then the central charge won't move.
 
No.. the charges are different. Q on corner A, 2Q on corner B, -3Q on corner C and 6Q on corner D. The charge that is put in the center of the square is Q..
 
If the four charges are fixed, you jujst need to find the U of the central charge Q.
 
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