Question

decide how the sketches below would be listed, if they were listed in order of decreasing force between the charges. that is, select \1\ beside the sketch with the next strongest force between the charges, and so on.
note for advanced students: since the units of each charge are not written, you may assume any convenient and reasonable unit, for example coulombs or multiples of e.

Explanation:

Step1: Recall Coulomb's Law

Coulomb's Law is \(F = k\frac{q_1q_2}{r^2}\), where \(k\) is a constant, \(q_1\) and \(q_2\) are charges, and \(r\) is the distance between them.

Step2: Analyze the first pair (top - left)

Let's assume the charge of the red particle is \(q_1=-e\) and the blue one is \(q_2 = +e\). The distance \(r_1\) (counting grid - squares) is relatively large.

Step3: Analyze the second pair (top - right)

The red particle has \(q_1=- 2e\) and the blue one has \(q_2=+e\). The distance \(r_2\) is larger than in some other cases. Using \(F = k\frac{q_1q_2}{r^2}\), \(F_2=k\frac{(-2e)(+e)}{r_2^2}\)

Step4: Analyze the third pair (bottom - left)

The red particle has \(q_1=-e\) and the blue one has \(q_2 = +e\). The distance \(r_3\) is smaller than \(r_1\) and \(r_2\). So \(F_3=k\frac{(-e)(+e)}{r_3^2}\), and since \(r_3|F_1|\) (because \(F\propto\frac{1}{r^2}\) when \(q_1q_2\) is constant in magnitude)

Step5: Analyze the fourth pair (bottom - right)

The red particle has \(q_1=-2e\) and the blue one has \(q_2=+e\). The distance \(r_4\) is the smallest. \(F_4=k\frac{(-2e)(+e)}{r_4^2}\). Comparing \(F_4\) and \(F_3\), since \(|q_1q_2|\) for the fourth pair (\(2e^2\)) is larger than for the third pair (\(e^2\)) and \(r_4 < r_3\), \(|F_4|>|F_3|\)

Answer:

Bottom - right (1), Bottom - left (2), Top - right (3), Top - left (4)