Three charges lie along the x-axis. One positive charge, q1 = 4.80*10^-18 C, is at x = 3.72 m, and another positive charge, q2 = 1.60*10^-19 C, is at the origin. At what point on the x-axis must a negative charge, q3, be placed so that the resultant force on it is zero?

The third charge needs to be placed at .

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:

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Similarly, the magnitude of the electrostatic attraction between and would be:

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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 :

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By the assumption that , it should be true that and . Therefore, .

Take the square root of both sides of the equation .

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Therefore:

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Hence, should be placed at .