Two point charges in free space are Q1=10nC at (5,0,0) and Q2= 25nC at (-5,0,0). Where shouldQ3=20nC be located such that the force on Q3 is zero
Question
Two point charges in free space are Q1=10nC at (5,0,0) and Q2= 25nC at (-5,0,0). Where should Q3=20nC be located such that the force on Q3 is zero?
Solution
The force on Q3 due to Q1 and Q2 must be equal and opposite for the net force to be zero.
Let's consider two possible positions for Q3: one along the line joining Q1 and Q2 to the right of Q1 (position A) and the other to the left of Q2 (position B).
- Position A (x,0,0) where x > 5:
The force on Q3 due to Q1 is given by Coulomb's law:
F31 = kQ1Q3/|r3 - r1|^2 = kQ1Q3/(x - 5)^2
Similarly, the force on Q3 due to Q2 is:
F32 = kQ2Q3/|r3 - r2|^2 = kQ2Q3/(x + 5)^2
For the net force on Q3 to be zero, F31 = F32. Therefore:
Q1/(x - 5)^2 = Q2/(x + 5)^2
Solving this equation will give the value of x for position A.
- Position B (-x,0,0) where x > 5:
Similarly, we can write:
Q1/(x + 5)^2 = Q2/(x - 5)^2
Solving this equation will give the value of x for position B.
Note: k is Coulomb's constant, r1, r2, and r3 are the positions of Q1, Q2, and Q3 respectively.
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