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 strongest force between the charges, select \2\ 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

The force between two charges is given by $F = k\frac{q_1q_2}{r^2}$, where $k$ is a constant, $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between them. Assume the distance between charges in each grid - square is the same unit distance.

Step2: Calculate the product $|q_1q_2|$ for each case

Case 1: $q_1=- 1$, $q_2 = + 2$, $|q_1q_2|=|(-1)\times(2)| = 2$.
Case 2: $q_1=-1$, $q_2 = + 1$, $|q_1q_2|=|(-1)\times(1)| = 1$.
Case 3: $q_1=-2$, $q_2 = + 1$, $|q_1q_2|=|(-2)\times(1)| = 2$.
Case 4: $q_1=-3$, $q_2 = + 1$, $|q_1q_2|=|(-3)\times(1)| = 3$.

Step3: Rank the forces

Since the force is proportional to $|q_1q_2|$ (with $r$ constant), the ranking from strongest to weakest force:
The fourth sketch has the strongest force ($|q_1q_2| = 3$), so it is 1.
The first and third sketches have the same non - maximum value of $|q_1q_2|=2$, we can rank them as 2 and 3 (arbitrarily, say first sketch is 2 and third is 3).
The second sketch has the weakest force ($|q_1q_2| = 1$), so it is 4.

Answer:

First sketch: 2
Second sketch: 4
Third sketch: 3
Fourth sketch: 1