Answer :
In order to make center voltage zero in a square configuration, -7C charge should be placed at the fourth point
So, the correct answer is: a. -7C.
To make the center voltage zero in a square configuration, the sum of the voltages at the four points connected to the center (which we'll call O) must equal zero.
Let's analyze the given voltages at the three points:
1. Voltage at the first point (10C): This contributes a positive voltage of 10C.
2. Voltage at the second point (12C): This contributes a positive voltage of 12C.
3. Voltage at the third point (-15C): This contributes a negative voltage of -15C.
Now, we need to determine the charge at the fourth point to balance these voltages.
Let's assume the charge at the fourth point is Q. If the distance between O and each of the four points is the same, then, by the principle of superposition, the voltage at O due to Q will be:
Voltage due to Q = kQ/r, where k is the electrostatic constant and r is the distance between O and the fourth point.
We want this voltage to cancel out the sum of the other voltages:
10C + 12C - 15C + kQ/r = 0
22C - 15C + kQ/r = 0
7C + kQ/r = 0
Now, we need -7C to balance the equation:
7C - 7C + kQ/r = 0
0 + kQ/r = 0
This means that if -7C charge is placed at the fourth point, it will create a voltage that cancels out the sum of the other voltages, resulting in a center voltage of zero.
Thus, the answer is: a. -7C.
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