Answer:
The third charge needs to be placed at .
Step-by-step explanation:
Both and would attract .
These two electrostatic attractions need to balance one another. Hence, they need to be opposite to one another. Therefore, and need to be on opposite sides of . That is possible only if is on the line segment between and .
Assume that is at , where (in other words, is on the line segment between and , and is away from .)
Let denote Coulomb's constant.
The magnitude of the electrostatic attraction between and would be:
.
Similarly, the magnitude of the electrostatic attraction between and would be:
The magnitudes of these two electrostatic attractions need to be equal to one another for the resultant electrostatic force on to be . Equate these two expressions and solve for :
By the assumption that , it should be true that and . Therefore, .
Take the square root of both sides of the equation .
Therefore:
Hence, should be placed at .
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