decide how the sketches below would be listed, if they were listed in order of decreasing force between the…

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 Coulomb's constant, $q_1$ and $q_2$ are the magnitudes of the charges, and $r$ is the distance between them.

Step2: Analyze the first - top - left sketch

Let the distance between the two charges of magnitude $|q_1|=|q_2| = 1$ be $r_1$. Then $F_1=k\frac{1\times1}{r_1^2}$.

Step3: Analyze the second - top - right sketch

The two charges are $|q_1| = 2$ and $|q_2|=1$. Let the distance between them be $r_2$. Then $F_2=k\frac{2\times1}{r_2^2}$.

Step4: Analyze the third - bottom - left sketch

The two charges of magnitude $|q_1|=|q_2| = 1$ and assume the distance between them is $r_3$. Since the grid is the same as the first sketch, if we assume the distance in the first sketch is $r_1$, and here the distance is larger than $r_1$ (by counting the grid squares), say $r_3>r_1$. Then $F_3=k\frac{1\times1}{r_3^2}$.

Step5: Analyze the fourth - bottom - right sketch

The charges are $|q_1| = 2$ and $|q_2| = 1$. Let the distance between them be $r_4$.

Step6: Compare the forces

Assume the grid squares represent a unit of distance. Comparing the magnitudes of the products $\frac{q_1q_2}{r^2}$ for each case. For the top - right sketch, with $q_1 = 2,q_2 = 1$ and a relatively small distance, it has the largest force. For the top - left and bottom - right sketches, the product $q_1q_2$ is 1 and 2 respectively, and the bottom - right has a smaller distance than the top - left in terms of grid squares, so the force in the bottom - right is larger than the top - left. The bottom - left has the smallest force as the charges are 1 and 1 and the distance is relatively large.

Answer:

Top - right: 1 Bottom - right: 2 Top - left: 3 Bottom - left: 4