Identical +7.99 ?C charges are fixed to adjacent corners of a square. What charge (magnitude and algebraic sign) should be fixed to one of the empty corners, so that the total potential at the remaining empty corner is 0 V?
Solution
The potential due to a point charge is kq/r where k is a constant equal to 9x10^9Nm^2/C^2 in MKS
If we call the length of each side D, the potential due to the two positive charges is
V = 7.99k/D(1/1 + 1/1.414) = 13.64k/D
The 3 rd charge will be at a distance D. Let us call it q.
Potential due to it = qk/D
For total potential to be zero:
13.64k/D + qk/D = 0
=> qk/D = -13.64k/D
=> q = -13.64 uC
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Identical +7-99 -C charges are fixed to adjacent corners of a square-.docx
1. Identical +7.99 ?C charges are fixed to adjacent corners of a square. What charge (magnitude
and algebraic sign) should be fixed to one of the empty corners, so that the total potential at the
remaining empty corner is 0 V?
Solution
The potential due to a point charge is kq/r where k is a constant equal to 9x10^9Nm^2/C^2 in
MKS
If we call the length of each side D, the potential due to the two positive charges is
V = 7.99k/D(1/1 + 1/1.414) = 13.64k/D
The 3 rd
charge will be at a distance D. Let us call it q.
Potential due to it = qk/D
For total potential to be zero:
13.64k/D + qk/D = 0
=> qk/D = -13.64k/D
=> q = -13.64 uC
